Template talk:Infobox probability distribution

1666:: I gave you some suggestions above about colors that are difficult for protanopes (someone missing the "red", i.e. long wavelength cone cell) to distinguish; I am protanopic, so this is accurate. In general the principle is simple: if you take any color and change the R value in its RGB, this change will be hard for a protanope to notice. It's a little trickier for the deuteranopes because (to simplify grossly) the green of RGB does not so well match the "green" cone cell that they are missing. However, the corresponding principle should be adequate for your purposes. 159: 141: 227: 209: 544:

distribution at a time. CDFs can be plotted using the floor function and one of the "steps" styles. Alternative, if only a single PMF is plotted, "impulses" is probably the best style to use. 3) I don't think including any kind of descriptive text is a good idea, because it renders the plots less useful for other editions of Knowledge, which may want to include their own descriptive text in French, Japanese, etc. A brief legend with formulas is fine, of course. --

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plotted, a table of parameter values and associated colors should be included on the plot. If one of the curves is "prototypical" or "standard", it should be in black. We want these plots to be usable in any language, so only numerals and mathematical symbols should appear in the image. Axes should be labelled with the appropriate symbols (x and p(x)/P(x) for PDF/CDF plots, k and p

1675:, I believe there are blue (RGB:0 0 1) and purple (1 0 1) lines that I can barely distinguish, red (1 0 0) and black (0 0 0) lines that I can distinguish slightly but not well, and a light colored line that could be either green (0 1 0) or yellow (1 1 0). As you can see, the difficulties encountered by a real, live protanope are predictable by the principle given above. 553:

and we definitely need the freedom to explain. I also added that the axes of an image need to be labelled (math symbols only). I notice that the mathematical symbols vary among the pages. Should there be some slight standardization, like p(a,b,c;x) for the PDF and P(a,b,c;x) for the CDF, with parameters a,b,c? I tentatively threw these into the specification too.

4473: 1729:) you/me/whomever picks a point (abscissa or ordinate) and then relates the order they appear to the legend on the graph. So for the normal cdf, I could say something like "at ordinate=0.3, the order of plots from left-to-right matches the legend top-to-bottom."? For most plots, there's some point where you can do this. For the 284:{{Infobox probability distribution | name = | type = | pdf_image = | cdf_image = | parameters = | support = | pdf = | cdf = | mean = | median = | mode = | variance = | skewness = | kurtosis = | entropy = | mgf = | char = }} 1779:

dashed. The colors that are likely to be confused are not that numerous, so you should be able to cover most confusing groups with two linestyles; use solid/dashed for pairs like red/black, blue/purple, green/yellow, red/brown, grey/cyan, grey/purple (see that's already way more lines than you need). --

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people? Or at least make a link to a color blind version? The most common color blindnesses by far are protanopia and deuteranopia. Protanopes require some distinguishing scheme for green/yellow, green/orange, green/brown, blue/purple, and cyan/grey. I'm not sure about deuteranopes, but I imagine

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Another problem is that the definition (or meaning) of entropy for the discrete and continuous pdf cases is really rather different. For a discrete random variable, the entropy is the minimum average amount of information necessary to exactly represent the value of the random variable. Thus, in this

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article, except that that article uses discrete distributions in its introductory examples and doesn't explicitly mention this integral. The above integral is also the definition that has been used in all other infoboxes (when it exists and can be expressed compactly). I don't see a reason for using

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My primary reasons for not wanting distribution in the infobox is that it a) takes up width of the template and will most likely cause it to wrap (ugh) and b) I don't see it as wholly necessary since the " distribution" is at the top of the page. Further point on b, I commonly say (and hear) things

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It is not too difficult to alter the colors of a PostScript file after the fact in a text editor. Maybe someone could come up with a palette of colors that is distinguishable by pretty much anyone, and we could convert the gnuplot-generated colors to that palette? A .ps file text-conversion script

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I really think that is wrong. X and x have to be from the same set. X is discrete, x must be discrete. I mean its wrong by dimensional analysis. X and x must have the same dimensions. For example, when dealing with income distribution, there are N people ranked by income, and X is R/N which means XN

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Whenever one of the fields is done using LaTeX math markup and the result converted to PNG rather than to HTML, the background is white, which clashes with the table background color. Is it possible to change either the table background or the rendering math background to be consistent or at least

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page. Michael Hardy and I have had a running discussion on the values of the uniform distribution at the transition points. I think we have settled the text aspect of the problem, but the PDF plot is at issue now. Most of the discussion page is devoted to our back and forth, so if people could read

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Will anyone still read this...? Cburnett, good point about the nerdiness of people reading these articles. Your colors solution is clever, but looking at the figures and imagining the caption you would have to add it seems a little laborious. My suggestion is the use of two linestyles, solid and

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I included the file naming convention you mentioned in the rewrite. I took out the "no caption" requirement in the template description of the pdf field, because by making the requirement of no text in the caption and no text in the image, we're boxed into having no explanation capabilities at all,

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I am setting the right-hand margin to zero for the infobox, by using the style coding "margin-right: 0em". Formerly, it had shifted the infobox to the left by about 4 letters (characters), causing the left-side text to be squeezed by 4 letters more narrow. This change should cause most articles to

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I don't think that discrete distributions even deal in the real number system, just integers, (or integral multiples of something) at least as far as the random variate is concerned. The CDF is undefined between the integers because the random variates are not selected from the real number system,

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You are correct that it is not the template itself. I don't know what I was thinking when I wrote that. Still I am curious why ";" has been used very consistently in the support intervals when people have used this template. If it is not common practice, I may end up changing it in the future but

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Well, we could make it a smaller font, put in line breaks for long ones, etc., but I favor keeping it rather than dropping it. My qualms remain, but its a style issue, not a true-false issue, so I'm not fanatical. Can we try to put another interested contributor on the spot as a tie breaker, e.g.

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My understanding of color blindness isn't the lack of ability to see colors, just that shades of red/green (or whatever) appear to be the same. So unless you have someone with color blindness on hand to determine if two colors appear the same then I don't see it as worth the time *guessing* what

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is extremely limited and not at all compatible with color deficient vision. I seem to recall that it is possible to use a small set of colors that most people can distinguish easily. Do you have any advice on which colors to use? This is assuming that we can get gnuplot to use colors specified by

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Upload Procedure - Images should be uploaded to the Knowledge commons. The file names should be of the form XXX_distribution_ZZZ.svg where XXX is the distribution name and ZZZ is either "PDF", "CDF", "PMF", or "CMF" depending on which function is plotted. The description page for the plots should

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Perhaps we should get everything else done first then worry about adding stuff? :) With the number of distributions I think it'll still be a fair amount of work just to get them all using the template with distribution plots and somewhat cohesive articles to boot. Otherwise, I'd like to see expo

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Yes, one could use "linespoints" style. However, that would look very similar to the plots of PMFs we have now and could be confusing. Probably best two either switch on "dashed" in gnuplot's PostScript "terminal", or to use the method you describe. Alternatively, one can put arbitrary labels on

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codes; e.g., #x03b8 for miniscule lambda. The axes of the plot should be in a ratio of 4 wide to 3 high. The size of the image should also be in a ratio of 4 wide to 3 high. The image should consist of a few distinct colors only, different curves having different colors. When multiple curves are

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Presently the template uses the notation such as "" to indicate an interval from 0 to 4 inclusive. I am not familiar with a semi-colon being used to denote an interval. I have always seen commas used (at least in English textbooks) such that the previous interval would be denoted by "". Is the

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I am adding new parameter "box_width" (default 325px) to allow narrowing the infobox to allow more left-side text. Also, new paramter "marginleft" sets the left-hand margin outside the infobox, by using the style coding "margin-left: 1em". Formerly, the infobox had always been shifted from the

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and I think including the exponential family form to would be a nice addition. It is true that even the exponential family page has only one distribution in the exponential family form, but I think this would be a worthwhile endevor for the wikipedia. I'm not sure how the specification of the

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I think it is an excellent idea, and have added it to a number of probability distribution pages that I am interested in. I have a problem with the idea of simply entering the name of the distribution without adding the words "distribution" after it. For example, the title of the exponential

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Comments: 1) In the past, we've used filenames of the form FOO_distribution_PDF.png (additional underscore/space before "PDF"). 2) Gnuplot "linespoints" style for discrete PMFs is a good idea. The alternative, using "impulses" or something similar, makes it difficult to display more than one

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for PMF/CMF plots. Further explanation should be made in the text caption for the image. Continuous distributions should be done as solid lines. Display of discrete distributions should use points connected by lines, with a short explanation in the caption (e.g."connecting lines do not imply

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Some value-at-risk type measures have been added to this template and then put into all the distribution pages. There's no reason for highly specialized fields like this to show up in the infobox for every distribution -- there are tons of other things that could be included in the infobox.

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software skip the documentation when formatting pages, and older versions could allow at least 10 copies of a medium-sized template to be used within one article, before the template-processing buffers filled with coding & documentation. The English Knowledge has been upgraded to skip

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I really don't like dashes or dotted lines. Sorry. :-) In my opinion they should only be used for special situations, like asymptotes of a function or whatever. Maybe we could come up with another scheme that doesn't look bad, like notating each plot with a symbol or something? -

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Basically, there is some disagreement as to the proper definition of the CDF and how to plot it. There is however, ample justification for the use of the "cumulative ogive" and since it is desireable to have multiple plots of the CDF that are easily readable, I favor the ogive plots.

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Parsons, "Statistical Analysis": Section 2.4 is titled "Graphic representations of frequency distributions" and lists only the "cumulative ogive" as a method of plotting the cumulative distribution function. Again, the cumulative distribution function examples are given as lists in

535:(I favor visible points connected by lines, with an explanation in the caption that the lines don't imply continuity. I know this goes against the "no caption" idea, but I really don't like losing the freedom to clarify things with a caption. Especially if we don't use axis labels! 1538:

means the probability that the expreiment yields a value less than or equal to r... Almost always r or x will be one of the numerical values which the experimaent can generate." All cumulative distribution functions for discrete variables are given as lists at the values of X. No

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Ok, I went to check my books and found the name of the plot is a "cumulative frequency polygon" or a "cumulative ogive". Please google these terms. With regard to the definition of the cumulative distribution function for discrete variables, the relevant books I checked say:

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left-side text by about 4 letters (characters), causing the left-side text to be squeezed by 4 letters more narrow. Those changes should not affect any articles, until those new parameters are specified within an article, to allow more text to the left-side of the infobox. -

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has units of people. If x is just any real number then we could have xN=3.7. 3.7 what? 3.7 people, but there's no such thing as 3.7 people. In Poisson statistics there is no such thing as 3.7 counts. It's like saying we need to define the CDF over the complex number plane.

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with essentially the same caption as for the PMF saying that the function is only defined for integer values. I don't think that's strictly true: I would have expected to see a step function that's constant almost everywhere except for non-continuous jumps at integers 0 to

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I've been looking to several probability distribution articles on Knowledge, and I'm surprised to see that the rendering of each probability and cumulative density function is not uniform, which can be unpleasant when you are trying to compare two functions side-by-side.

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These suggestions cover cases of dichromats, people missing one cone entirely. Another common form of red/green color blindness is anomalous trichromacy, people with all three cones but messed up spectra. I don't think your plots should be too problematic for anomalous

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I understand that the infobox text reads "Name: Exponential" and that makes sense, but what is displayed is just "Exponential" and that makes no sense, its an adjective thats missing a noun to modify. Alternatively, we could change the infobox to display "{{{name}}}

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I was about to make some Zipf and Zeta distribution plots, and I was thinking it would be very informative to plot these PMF's on a log-log scale, where they become straight lines. Assuming there's an explanation in the caption, does this sound like a good idea?

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Looking at examples of use for Desktop and Mobile, there seem to be two small issues on the mobile version: (1) odd positions of dividers within some rows compared to the other rows and (2) disappearing borders of the final row actually used. For example in

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Sorry this is so pedantic; probably there should be a more central WP color blindness styleguide for creating graphics; then I would only have to rant about this in one place. If anyone knows where and how to make this happen I will be happy to contribute.

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I guess I prefer the italics but tex interprets the hyphen as subtraction (first inv-gamma) but putting the hyphen into an \mbox{} makes it look better (second inv-gamma). So going italics would mildly complicate names unless we drop the hyphen altogher:

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One problem with the definition of entropy in the infobox template is that there is a lack of clarity regarding the units – i.e., the scaling. Especially for discrete pdfs, most people tend to think of entropy as something to be measured in units of

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For confusing colors, differ them in saturation and brightness in addition to differing them in hue. For example, rather than just blue=(0 0 1) and purple=(1 0 1), use blue=(0 0 .5) purple=(1 .5 1). For red and black, use (1 .25 .25) and (0 0 0).

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I have updated the instructions for Standard Plots to reflect Wikimedia's preference for Scalable Vector Graphics (SVG). These are actually easier to create in Gnuplot using terminal svg. They are more useful than png or other rasterized formats.

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page. Following the list is an additional category "unclassified" which have not yet been entered into the probability distribution page, and need to be. The status of each page is given by the letters following the name of the page

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are zeta-distributed. My question is - what is the name of this distribution? "Compound Poisson/zeta" or what?. In general, if XXX is the name of a distribution, whats the name of the compound Poisson distribution over XXX? Thanks -

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Regarding side point: most people that would be genuinely interested in generated pdfs/pmfs and cdfs of distributions are likely to know of a way to generate plots (either through gnuplot or matlab or some of the statistical

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The template doesn't enforce any particular formatting for the support intervals (and in fact, support is rarely an interval). If you feel the commas are more appropriate, feel free to edit the support value in the infobox.

3759:(as given above) and is somewhat different. In this case, the expected amount of information necessary to exactly represent the value of the random variable is generally infinite. Thus, in the continuous case, the entropy 1658:: Even considering that I personally have run octave at some point in my life, I think that assuming everyone (anyone?) will be able and willing to generate his/her own plots given the source is absurdly optimistic :)... 1588:

I uploaded the Zipf plots, but inadvertently labelled the CMF horizontal axis with k. Before I fix it, can anyone remind me of the reason for not labelling axes? Is it just to maintain flexibility in the text notation?

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Though I have talked to some people on IRC and know it won't happen any time soon, but it'd be neat to have an online pdf/cdf generator using gnuplot or something. Put in the distribution and parameters and plot it.

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I mean, if you were writing a paper on the exponential distribution, would you title it "exponential? Even if its a name, like Poisson, its a modifier. Are there hidden benefits to having a poorly written title?

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arbitrary RGB triples. Failing that, one could use dashed and dotted lines. In any case, we're rapidly approaching the point where we need to automate the creation of these plots. Does anyone have experience with

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of the normal: "the plots with the peak at 0 are the top 3 plots in the legend in the same order; the bottom legend entry is the plot with peak at -2" Basically describing the plots instead of marking up the

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but from the integer number system, (or equivalently some real # time the integers). I looked at the CDF article and it only talks about continuous distributions. Maybe we should write an article for CMF's.

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4. If 1, I can also go and work out this value for other distributions, and add it there, e.g. Binomial, Poisson, you name it. Does anyone see a specific distribution that I should add it to also, → make a

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I like it. I've been meaning to work on these articles and to fill in all those details. Let's start with the most important distributions and also create some missing articles about the less common ones.

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Right, I'm peripherally aware of the issue, especially concerning red/green color blindness (forget what it's called, if only I had an encyclopedia…). Unfortunately, the choice of colors provided by

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wikipedia page should connect to laypeople as much as it does to statisticians. I agree also, however that changing a (this) template is no small deal, that's why I'm stopping by here to ask. So:

3798:. The number of elements in the sum is a Poisson-distributed variable. For every probability distribution, there will be a compound Poisson version. The one I was working on was one in which the X 1743:

Though, now that I think of it, isn't it easy in gnuplot to add marks to lines and they show up in the legend? (By marks I mean symbols on top of a solid line, not using dotted or dashed lines).

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Why this warning message: "Warning: Page using Template:Infobox probability distribution with unknown parameter "value_at_risk" (this message is shown only in preview)." appears at this page "

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Thanks for your work on these graphics; they look great. I have a gripe though (sorry): could you guys use dashed/dotted/marked lines for the different colors in recognition of the needs of

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The purpose for the template is to consolidate the basic information in one spot since it seems rather spotty and inconsistent across the distribtion articles. Please give me some feedback.

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I think MarkSweep or CBurnett added this to the template, we should ask them what they had in mind. I have had a question about this too, because the entropy is defined in the template as:

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It should be mentioned that this warning is ignored but appears when we are in "Preview" page, and I cannot find the "value_at_risk" parameter in this template to resolve it. Any idea?

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plots, which would require manual intervention. Overall I think "dashed" output and/or using a safer set of colors that vary on more than one dimension would be the best choice. --

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I believe I tried to find a way to change the math background some time ago but never succeeded, so suspect the table would be where it is possible. Any thoughts or suggestions?

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which explicitly states the parameters, their order, and the variable used for the support. Though, for binomial I've also see "Bin". It's just whatever we want to set, I guess.

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template-documentation text since January 2008. Documentation text has always been omitted before displaying an article page over the Internet (unless editing the template).

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Lindgren, "Statistical Theory": Theres no concise quote, but its clear that the CDF is defined as a continuous function on the real number line. Plots are done accordingly.

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be interpreted as the amount of information conveyed per sample. The interpretation of what "entropy" means in the continuous case is more difficult and obtuse (involving

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That sounds fine. On a related topic, should there be an entry in the infobox to inform about these names? Perhaps the first entry after the plots could be "Formula:

3387:(though all this about distributions is just a subset of probability so I think it merits its own project...but not if we're going to set notation of distributions). 2438:

like "Let X be gamma" or "Let X be gaussian" since "distribution" is understood and, thusly, implicit. I have no qualms with excluding distribution from the infobox.

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I like that caption method you used. I prefer p(x) and P(x) (p for probability) but if you have any argument against it, lets do f(x) and F(x). For the parameters,

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section above (Bit late for DFH I suspect). It should be straightforward to make another subpage e.g. for singular distributions, if someone really wants to. --

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Alternatively, for confusing colors differ the line style, so for blue and purple, make one dashed. Likewise for red and black, yellow green and orange, etc.

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case, the entropy can be interpreted as the amount of information conveyed per sample of the random variable. For the continuous case, entropy is defined as

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distribution infobox should read "exponential distribution" not just "exponential". Replicating what I wrote on the exponential distribution discussion page:

481: 4376:, I would have to add it here / to this template first. I argue that as this metric is more frequently used by laypeople than e.g. variance, and I feel the 5018: 5023: 4056:

I have put a limited amount of documentation inside the template, to be displayed (as typical) during the template stand-alone mode. New versions of the

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is defined on the real line and can use the same definition of cdf as the continuous RV's. But they seem to generally not write the otherwise condition.

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for discrete distributions. So the label of the horizontal axis should be obvious. (Though I realize that repeating the obvious wouldn't hurt either.) --

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they *might* see. Also, with providing source then anyone could generate their own plots (though not everyone will be able to, at least it's a start).

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I'm not an expert at data visualization, and I have no preference over what style to use, as long as it is consistent across all distributions.

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Regarding main point: finally, someone complaining about color choice that is color blind! :) How's this for an idea: on each image page (i.e.,

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It would be useful if functions related to the distributions in languages such as R and SAS were included in this infobox. For instance, see

1579:(which I should re-do to match the standard style). Perhaps do both linear scale and double log scale plots for these three distributions? -- 243: 91: 3928: 3539:

I think it was me who added that entry to the infobox template. The definition of the entropy functional I've been using is the following:

1444:{\displaystyle f_{X}(x)=P(X=x)=\left\{{\begin{matrix}(1-p)^{x-1}p&{\mbox{for x=1,2,...}}\\0&{\mbox{otherwise}}\end{matrix}}\right.} 175: 3727:

article uses a mixture of the two, so linking to it in the infobox label does not clarify which is intended. Note, for example, that the

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Whether you want to muck up your current graphs or create alternative colorblind versions and then somehow link to those, up to you.

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I was playing around with a compound Poisson distribution, which is the sum of a number of identically distributed variables X

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I would prefer p(x) for pdf/pmf and P(x) for cdf and to use the captions I made for Normal (external to image in small font).

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1. What do others here think? Should/may I add this field to the template, and fill it out for the normal distribution?

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2. What should we call it? I suggest MAD for short as this abbreviation is used frequently, and direct the link to

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should be created to specifically address pdf/pmf supports. (Posting this here since I won't get to it for a bit.)

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semi-colon in common use in statistics? My experience in analysis is such that I have only come across the comma.

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If any of these don't exist, then put "Does not exist" (or something to the same effect); leave blank if unknown.

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I think we should add the option to include statistical estimates of parameters of the distributions, namely the

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Is this the right kind of entropy in this context? Maybe "free entropy" should be used instead? (Michael Hardy)

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Also, every reference I checked uses f(x) and F(x) as the PDF and CDF, so I think I will change my mind on that.

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Actually, I changed the order: parameters first; then support (which may depend on the parameters, e.g. for the

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for the CDF in the articles themselves. Or perhaps use a more descriptive and/or conventional name instead of

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family, conjugate prior if it has one, sufficient statistic for N samples, and anything else we can think of.

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I guess I'm out of practice with templates. I put in the quantile function as an option, entered it in the

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To use this template, put this in the article and fill it in as appropriate (see below code for detail):

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function", which is then made into a wikilink. When there is no type entry or one besides those two (

2584:?" Can't imagine that it'd be fun/easy to work that into each article. Easier to be in the infobox. 226: 208: 17: 4807: 4599: 4300: 4295: 4285: 3982: 3756: 2606: 2539: 2490:, and I don't see how the full title would fit in an infobox, which shouldn't be wider than 350px. -- 2311: 2227: 2198: 2181: 2143: 2120: 1980: 1974: 951: 734: 566: 4191: 4915: 4606: 4558: 4402: 4377: 4373: 4280: 4230: 4195: 3963: 3944: 3913: 3869: 3861: 3824: 3724: 3694: 3523: 2353: 2336: 2250: 2222: 2192: 2137: 2067: 1918: 1603: 867: 630: 577: 562: 469: 61: 3221:

Well, since no one gave input: I'm using no italics using \mathrm or \mbox (if there's a hyphen).

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on Knowledge. If you would like to participate, please visit the project page, where you can join

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on Knowledge. If you would like to participate, please visit the project page, where you can join

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errors in the code but the message isn't seen. Is there something improper about this usage? Is

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over at Wikibooks. Given chemboxes as a precedent, there is more than enough room for this info.

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I think what is happening here is that this construction splices the entry in the "type" field (

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which looks more consistent between rows. (Same thing using Firefox/Chrome/Edge on a desktop)

4333:: Please do not use the inane phrase "cumulative density function." There is such a thing as a 2569:; then the pdf and cdf formulas, which depend both on the parameters and the support/domain. -- 4584: 4220: 4104: 4069: 4039: 4016: 3842: 3748: 3720: 2670:

These two are used in the template to only show "PDF" or "PMF" depending on the distribution:

2513:

Ok, I accept the will of the majority but I reserve the right to complain endlessly about it.

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I believe this is perhaps more practically relevant than measures like "skewness". Thoughts?

4486: 4126: 4085: 3823:

natural parameter should be handled, another field or in the exponential family form field.

2055: 3639:{\displaystyle \mathrm {\mathrm {H} } (f)=-\int _{-\infty }^{\infty }f(x)\,\ln(f(x))\,dx\!} 4803: 2593: 2428:

Discussion is more relevant on this talk page instead of an individual distributions page.

1611: 1460: 463: 2694:? I don't think I've ever actually seen a plot of the pdf so I'm not sure it's correct. 368: 4565: 4245: 4171: 3973:

It would be worthwile to add these fields, especially since for some distributions the

3959: 3940: 3909: 3887: 3865: 3706: 3282: 2654: 2610: 2597: 2570: 2555: 2491: 2421:

P.S. to Cburnett - sorry if there was any aggravation, I didn't know this page existed.

2387: 2079: 1861:

The status is not up to date!!! Please bring it up to date as you check out the pages.

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of the distribution, which may depend on the parameters. Specify this as "<math: -->

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There's a lot of distribution to cover, in my opinion the most common ones would be:

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they would have trouble with red/orange, red/yellow, blue/cyan, and purple/grey. --

561:

Regarding captions, they can be added below plots outside the image. Have a look at

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Actually, I would just assume drop the name from the infobox than clutter it up...

516:

continuity"), unless a single plot is used, in which case "impulse" plots are best.

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I didn't add it for the Binomial however, as that formula is quite unwieldy (see

4182:

Proposal to add corresponding computer functions in common statistical languages;

1912: 4481: 1836:

The following is a list of probability distribution pages, as classified by the

4853:, which is kind of the "default" estimation method. This would assume a vector 848:

I'm not sure if axes need to be labeled. We've been fairly consistent in using

3735:

articles seem to be currently reporting entropy in units of bits, whereas the

239: 3409:

the discussion and put in their two cents, I think we can settle this issue.

2486:

on this, purely for reasons of space. We have articles with long titles like

4598:

I tend to add parameters "raw moments" and "central moments", with links to

4167: 4057: 3883: 171: 3743:

articles seem to be using units of nats. I suggest to expressly state "(in

310:

The following should all be tex equations and exclude any function labels (

4823: 4394:

3. Can anyone help me on how I do this, or should I figure it out myself?

4152: 3955: 3804: 3527: 3410: 2703: 2514: 2464: 2413: 1590: 1568: 1559: 1296: 969: 934: 918: 554: 536: 526:". When done using gnuplot, the relevant instructions should be included. 457: 451: 1124:. I don't think there is a need to define a separate notion of a CMF. -- 1624: 503: 4451:

Can someone add a moments2 parameter, perhaps? See my recent hack at

3958:

generating function is also worthwhile considering for the template.

439: 304:"pdf_image" should be a full wikicode for an image (including the "]" 4064:

Feel free to revise or reduce that documentation in the template. -

365:"parameters" should be the parameters for the distribtion (such as 933:

I will leave the specification as it stands, then, using p and P.

294:"type" should be either "density" or "mass", which corresponds to 4986:{\displaystyle {\hat {\mu }}={\frac {1}{n}}\sum _{i=1}^{n}x_{i}} 1804:

could probably be made by someone who knew what they were doing.

1629: 433: 3744: 3716: 103: 26: 3509:{\displaystyle S=\int _{-\infty }^{\infty }f(x)\ln(f(x))\,dx} 1851:

C - has all relevant infobox entries filled other than images

832:{\displaystyle \mathrm {Gamma} (\lambda \,|\,\alpha ,\beta )} 4792:{\displaystyle E=\exp \left(k\mu +k^{2}\sigma ^{2}/2\right)} 3931:, I had the idea of allow a field in this template for the 3719:; however, it is sometimes more convenient to use units of 2592:

Good idea. Perhaps a combination of that and a link to the

1438: 1854:

D - has gnuplot code in the above image description pages

950:

Another thing though: I saw you added a CMF plot for the

522:

contain a short description, the GFDL tag, and a link to

3090:{\displaystyle X\sim {\mbox{Inv-Gamma}}(\alpha ,\beta )} 3045:{\displaystyle X\sim Inv{\mbox{-}}Gamma(\alpha ,\beta )} 2538:

should be added right above parameters. Though, I think

778:

for the standard normal CDF. I've also used things like

498:

Construction - Standard plots should now be produced in

4571:

but there is no error message displayed. There are two

3855:, "mass" or "density") into "Probability <blank: --> 3204:{\displaystyle X\sim {\mbox{InvGamma}}(\alpha ,\beta )} 4824:

https://en.m.wikipedia.org/Wrapped_Cauchy_distribution

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of i.i.d. samples taken from the given distribution.

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Knowledge:How to create graphs for Knowledge articles

1506: 1463: 1326: 1255: 1142: 1084: 988: 870: 784: 737: 690: 633: 580: 421:" for continuous distributions, and as "<math: --> 391: 371: 320: 4828:

https://en.wikipedia.org/Wrapped_Cauchy_distribution

3985:), even if it is—more or less—trivial to compute. -- 2910:{\displaystyle X\sim {\mbox{Gamma}}(\alpha ,\beta )} 287:

Fields (data goes between the equal size and pipe):

238:, a collaborative effort to improve the coverage of 170:, a collaborative effort to improve the coverage of 4079:

Formating of support intervals: why the semi-colon?

3837:One of the box items points to a non-existing page 1231:{\displaystyle P(x)=\Pr=\sum _{k\leq \Re (x)}p(k).} 4985: 4903: 4791: 4688: 4011:allow more text to the left-side of the infobox. - 3723:, which is what is done in the formula above. The 3685: 3638: 3522:and I don't see that definition explicitly in the 3508: 3358: 3273: 3203: 3158: 3089: 3044: 2975: 2909: 2864: 2811:{\displaystyle X\sim {\mbox{N}}(\mu ,\sigma ^{2})} 2810: 2758: 2280:Two or more random variables on same sample space 1530: 1476: 1443: 1287: 1230: 1116: 1058: 909: 831: 770: 723: 672: 619: 404: 377: 354: 2642:Standard Layout for Probablity Distribution Pages 1848:B - has standardized plots of PDF/PMF and CDF/CMF 3359:{\displaystyle X\sim \mathrm {Binomial} (k;n,p)} 1500:Guenther, "Concepts of Statistical Inference": " 1158: 1004: 4429:http://mathworld.wolfram.com/MeanDeviation.html 3634: 3381:Knowledge:WikiProject Probability distributions 2976:{\displaystyle X\sim Inv-Gamma(\alpha ,\beta )} 1796:A guide for creating plots has been started at 3878:I've just noticed that the key to this is the 3296:To be pedantic, I would prefer something like 3159:{\displaystyle X\sim InvGamma(\alpha ,\beta )} 3703:, just because it arises primarily in physics 1059:{\displaystyle P(x)=\Pr=\sum _{k\leq x}p(k).} 8: 4455:(and recent talk there) for why we want it. 2702:I plotted them and, by eye, they look fine. 4151:, but it did not show up. How to fix this? 3526:article. By the way, what is free entropy? 2865:{\displaystyle X\sim Gamma(\alpha ,\beta )} 1295:. Not only that, it screws up the plots :) 841:exponential distribution#Bayesian inference 4431:). Should I delete this section now? Best 4341:, but "cumulative" contradicts "density". 4003:Narrowing right-side margin for wider text 203: 135: 4977: 4967: 4956: 4942: 4928: 4927: 4925: 4892: 4867: 4858: 4776: 4770: 4760: 4724: 4712: 4659: 4647: 4629: 4617: 3977:cannot be found anywhere in the article ( 3655: 3582: 3574: 3549: 3548: 3546: 3456: 3448: 3436: 3309: 3301: 3239: 3237: 3179: 3171: 3109: 3065: 3057: 3005: 2988: 2923: 2885: 2877: 2824: 2799: 2779: 2771: 2759:{\displaystyle X\sim N(\mu ,\sigma ^{2})} 2747: 2723: 1505: 1468: 1462: 1427: 1411: 1394: 1374: 1331: 1325: 1263: 1262: 1254: 1192: 1141: 1092: 1091: 1083: 1029: 987: 882: 869: 810: 785: 783: 749: 736: 702: 689: 645: 632: 592: 579: 524:Category:Probability distributions images 396: 390: 370: 343: 319: 120:does not require a rating on Knowledge's 4026:New parameters: box_width and marginleft 3693:. This is how entropy is defined in the 4997:2A00:11B1:10A0:D19C:9054:5C53:7422:B130 4832:2A00:23C6:148A:9B01:19D3:4402:D4CF:3421 4205:Uniform probability distribution graphs 3660: 3626: 3600: 3498: 2488:Scaled-inverse-chi-squared distribution 2162:scaled-inverse-chi-squared distribution 887: 880: 815: 808: 754: 747: 707: 700: 650: 643: 597: 590: 205: 137: 4576: 4049:Put some documentation inside template 3900:background color clashes with math png 3839:Template:Probability distribution/link 3698:a different notion of entropy for the 3406:Talk:Uniform distribution (continuous) 2649:Knowledge talk:WikiProject Probability 2580:Now, how about a yes/no answer to "In 2211:Generalized extreme value distribution 18:Template talk:Probability distribution 4372:, and was informed to that to add it 3274:{\displaystyle \mathrm {Binom} (n,p)} 2052:Supported on semi-infinite intervals 1800:. It is mostly about gnuplot so far. 1314:) defines the pmf — pedantically — as 355:{\displaystyle f(x;\mu ,\sigma ^{2})} 232:This template is within the scope of 164:This template is within the scope of 109: 107: 7: 4689:{\displaystyle E=\sigma ^{n}(n-1)!!} 3772:2001:4898:E0:2019:B581:94D:4C40:2BDC 2002:Continuous univariate distributions 1575:Absolutely. I did the same for the 980:it's customary to define the CDF as 2690:Can anyone verify the pdf image at 2234:Levy skew alpha-stable distribution 2110:noncentral chi-squared distribution 1959:(special case of negative binomial) 126:It is of interest to the following 34:for discussing improvements to the 5019:Template-Class Statistics articles 3583: 3578: 3550: 3457: 3452: 3331: 3328: 3325: 3322: 3319: 3316: 3313: 3310: 3252: 3249: 3246: 3243: 3240: 2715:Should this be italicized or not? 2327:Hotelling's T-squared distribution 1870:Discrete univariate distributions 1288:{\displaystyle P:\mathbb {R} \to } 1199: 1170: 1117:{\displaystyle P:\mathbb {R} \to } 798: 795: 792: 789: 786: 738: 25: 5024:NA-importance Statistics articles 4904:{\displaystyle (x_{1},...,x_{n})} 4504:Unknown parameter "value_at_risk" 4405:and 4: for binomial distribution. 4368:or as mathematicians call it the 3385:Knowledge:WikiProject Probability 2554:I concur. I'm adding this now. -- 1727:Image:Normal distribution cdf.png 852:for continuous distributions and 4471: 4339:cumulative distribution function 3923:Probability generating function? 2544:Support (mathematics)#Statistics 2295:multivariate normal distribution 2092:inverse-chi-squared distribution 2005:Supported on a bounded interval 771:{\displaystyle \Phi (x\,|\,0,1)} 731:for the standard normal PDF and 252:Knowledge:WikiProject Statistics 225: 207: 157: 139: 108: 51:Click here to start a new topic. 36:Infobox probability distribution 5029:WikiProject Statistics articles 3933:probability-generating function 3650:with the added convention that 2009:continuous uniform distribution 976:For a discrete random variable 307:"cdf_image" same as "pdf_image" 255:Template:WikiProject Statistics 184:Knowledge:WikiProject Infoboxes 4933: 4898: 4860: 4840:08:42, 29 September 2023 (UTC) 4730: 4717: 4677: 4665: 4652: 4641: 4635: 4622: 4515:"? And how we can resolve it? 3818:Many distributions are in the 3700:Wigner semicircle distribution 3674: 3668: 3623: 3620: 3614: 3608: 3597: 3591: 3561: 3555: 3495: 3492: 3486: 3480: 3471: 3465: 3353: 3335: 3268: 3256: 3198: 3186: 3153: 3141: 3084: 3072: 3039: 3027: 2970: 2958: 2904: 2892: 2859: 2847: 2805: 2786: 2753: 2734: 2647:I suggest we continue this on 2596:distribution, if available? -- 2217:hyperbolic secant distribution 2045:Wigner semicircle distribution 2017:ABCDE (needs some copyediting) 1963:negative binomial distribution 1940:Maxwell-Boltzmann distribution 1525: 1513: 1391: 1378: 1364: 1352: 1343: 1337: 1282: 1270: 1267: 1222: 1216: 1208: 1202: 1182: 1179: 1173: 1161: 1152: 1146: 1111: 1099: 1096: 1050: 1044: 1019: 1007: 998: 992: 910:{\displaystyle f(x\,|\,a,b,c)} 904: 883: 874: 826: 811: 802: 765: 750: 741: 718: 703: 694: 673:{\displaystyle F(x\,|\,a,b,c)} 667: 646: 637: 620:{\displaystyle f(x\,|\,a,b,c)} 614: 593: 584: 574:About the formulas, I've seen 349: 324: 187:Template:WikiProject Infoboxes 1: 4812:22:36, 17 February 2023 (UTC) 4370:first absolute central moment 4362:Normal Distribution Talk Page 4351:15:22, 23 December 2019 (UTC) 4322:09:15, 5 September 2018 (UTC) 4074:15:25, 22 February 2009 (UTC) 4044:15:25, 22 February 2009 (UTC) 4021:15:25, 22 February 2009 (UTC) 3995:14:40, 27 February 2009 (UTC) 3968:15:07, 4 September 2008 (UTC) 3949:14:27, 4 September 2008 (UTC) 3892:11:53, 10 February 2008 (UTC) 3879: 2189:Supported on whole real line 1883:discrete uniform distribution 1671:For example, in the plots at 423:" for discrete distributions. 246:and see a list of open tasks. 178:and see a list of open tasks. 48:Put new text under old text. 4531:08:33, 15 October 2020 (UTC) 4441:22:44, 16 January 2020 (UTC) 4419:20:42, 12 January 2020 (UTC) 4360:Hi all! I'm coming from the 4356:Mean Average Deviation Added 4335:probability density function 2308:Matrix-valued distributions 1857:E - uses "standard" notation 1245:can be a complex number and 724:{\displaystyle N(x\,|\,0,1)} 422:k \in some set</math: --> 420:x \in some set</math: --> 412:for the normal distribution) 296:probability density function 4851:maximum likelihood estimate 4547:21:03, 25 August 2023 (UTC) 4498:02:13, 13 August 2020 (UTC) 4465:01:02, 13 August 2020 (UTC) 4188:binomial distributions in R 3874:20:10, 21 August 2007 (UTC) 3686:{\displaystyle 0\,\ln(0)=0} 2658:03:22, 19 August 2005 (UTC) 2277:Multivariate distributions 2205:Fisher-Tippett distribution 2177:inverse-normal distribution 2104:noncentral chi distribution 1901:hypergeometric distribution 1602:Discussion moved here from 1531:{\displaystyle Pr(X\leq r)} 405:{\displaystyle \sigma ^{2}} 56:New to Knowledge? Welcome! 5045: 4389:average absolute deviation 4125:I'll wait for more input. 3918:18:45, 15 April 2008 (UTC) 3846:10:40, 31 March 2007 (UTC) 3828:17:02, 24 April 2006 (UTC) 3404:We need some input on the 3217:17:25, Apr 13, 2005 (UTC) 2692:Inverse-gamma distribution 2482:I'm inclined to side with 2317:matrix normal distribution 2263:type-1 Gumbel distribution 2168:type-2 Gumbel distribution 2098:inverse-gamma distribution 2027:Raised cosine distribution 1945:Bose-Einstein distribution 1827:16:10, 16 April 2009 (UTC) 1812:22:44, July 24, 2005 (UTC) 539:05:12, 10 Apr 2005 (UTC)) 476:moment generating function 5005:10:06, 30 July 2024 (UTC) 4589:01:09, 13 July 2021 (UTC) 4200:05:21, 14 July 2018 (UTC) 4176:11:09, 11 June 2014 (UTC) 4161:01:06, 11 June 2014 (UTC) 3413:03:10, 25 Apr 2005 (UTC) 3391:06:41, Apr 24, 2005 (UTC) 3379:Maybe it's time to start 3225:05:14, Apr 24, 2005 (UTC) 2698:05:44, Apr 7, 2005 (UTC) 2635:03:54, Apr 11, 2005 (UTC) 2588:00:28, 24 Mar 2005 (UTC) 2550:02:57, 21 Mar 2005 (UTC) 2381:02:19, 10 Mar 2005 (UTC) 2246:noncentral t-distribution 2127:log-logistic distribution 2116:noncentral F-distribution 1784:11:57, 15 July 2005 (UTC) 1747:17:40, Apr 13, 2005 (UTC) 1648:03:42, Apr 11, 2005 (UTC) 1619:01:25, 11 Apr 2005 (UTC) 1593:01:33, 23 Apr 2005 (UTC) 1571:21:07, 20 Apr 2005 (UTC) 1562:05:11, 12 Apr 2005 (UTC) 1488:00:23, Apr 12, 2005 (UTC) 1299:16:10, 11 Apr 2005 (UTC) 1074:can be a real number and 972:01:58, 11 Apr 2005 (UTC) 937:00:04, 11 Apr 2005 (UTC) 929:22:37, Apr 10, 2005 (UTC) 921:20:26, 10 Apr 2005 (UTC) 627:used for the PDF/PMF and 557:12:36, 10 Apr 2005 (UTC) 300:probability mass function 220: 152: 134: 86:Be welcoming to newcomers 4579:a required parameter? – 4149:Exponential distribution 3927:Per a discussion on the 3833:Template needs repairing 3807:01:15, 7 Jun 2005 (UTC) 3741:exponential distribution 3710:20:59, 21 May 2005 (UTC) 3531:11:10, 21 May 2005 (UTC) 3285:05:47, 24 Apr 2005 (UTC) 2573:22:01, 23 Mar 2005 (UTC) 2558:21:48, 23 Mar 2005 (UTC) 2390:07:17, 10 Mar 2005 (UTC) 2359:Exponential distribution 2349:I put this template on: 2300:multinomial distribution 2257:Student's t-distribution 2074:exponential distribution 2062:chi-squared distribution 2021:Kumaraswamy distribution 1969:logarithmic distribution 1950:Fermi-Dirac distribution 1838:probability distribution 1763:19:35, 13 Apr 2005 (UTC) 1708:10:12, 11 Apr 2005 (UTC) 1636:02:05, 11 Apr 2005 (UTC) 1583:23:07, 20 Apr 2005 (UTC) 1249:is then a step function 1128:02:48, 11 Apr 2005 (UTC) 1078:is then a step function 963:00:24, 11 Apr 2005 (UTC) 945:00:24, 11 Apr 2005 (UTC) 860:19:39, 10 Apr 2005 (UTC) 548:06:07, 10 Apr 2005 (UTC) 500:Scalable Vector Graphics 415:"support" should be the 4914:So for example for the 4702:log-normal distribution 4513:Log-normal distribution 4135:20:53, 9 May 2010 (UTC) 4116:19:44, 9 May 2010 (UTC) 4094:19:33, 9 May 2010 (UTC) 3790:Compound Poisson - help 3780:20:55, 8 May 2013 (UTC) 2706:12:07, 7 Apr 2005 (UTC) 2613:01:42, 9 Apr 2005 (UTC) 2600:23:49, 7 Apr 2005 (UTC) 2530:Addition field: support 2517:06:33, 2 Apr 2005 (UTC) 2494:04:15, 2 Apr 2005 (UTC) 2467:19:30, 1 Apr 2005 (UTC) 2451:19:03, 1 Apr 2005 (UTC) 2416:17:29, 1 Apr 2005 (UTC) 2374:to test how it looked. 2132:log-normal distribution 2033:triangular distribution 1987:Yule-Simon distribution 1907:Rademacher distribution 1877:degenerate distribution 1577:Yule-Simon distribution 1303:Casella & Berger's 482:characteristic function 4987: 4972: 4905: 4793: 4690: 4594:Raw or central moments 4573:{{Error|Unknown type}} 4366:mean average deviation 3765:rate–distortion theory 3737:Bernoulli distribution 3729:geometric distribution 3687: 3640: 3510: 3360: 3275: 3205: 3160: 3091: 3046: 2977: 2911: 2866: 2812: 2760: 2290:Ewens sampling formula 2284:Dirichlet distribution 2039:von Mises distribution 1957:geometric distribution 1930:Boltzmann distribution 1926:With infinite support 1889:Bernoulli distribution 1532: 1478: 1445: 1289: 1232: 1118: 1060: 911: 833: 772: 725: 674: 621: 406: 379: 356: 314:function portion like 235:WikiProject Statistics 81:avoid personal attacks 4988: 4952: 4906: 4794: 4691: 4409:Cheers & thanks! 3733:binomial distribution 3688: 3641: 3511: 3361: 3276: 3206: 3161: 3092: 3047: 2978: 2912: 2867: 2813: 2761: 2567:binomial distribution 2536:Support (mathematics) 2322:matrix t-distribution 2240:logistic distribution 2150:Rayleigh distribution 1895:binomial distribution 1533: 1479: 1477:{\displaystyle f_{X}} 1446: 1305:Statistical Inference 1290: 1233: 1119: 1061: 912: 834: 773: 726: 675: 622: 565:or my recent edit to 407: 380: 357: 167:WikiProject Infoboxes 4924: 4857: 4817:Layout bug on mobile 4711: 4616: 4609:has central moments 4600:Moment (mathematics) 4364:. I was missing the 3983:Poisson distribution 3757:differential entropy 3654: 3545: 3435: 3400:Uniform Distribution 3383:or move this all to 3300: 3236: 3170: 3108: 3056: 2987: 2922: 2876: 2823: 2770: 2722: 2607:sufficient statistic 2540:Support (statistics) 2333:Other distributions 2312:Wishart distribution 2228:Laplace distribution 2199:Dirac delta function 2182:Weibull distribution 2144:Pearson distribution 1981:Skellam distribution 1975:Poisson distribution 1873:With finite support 1680:My suggestions are: 1504: 1461: 1324: 1253: 1140: 1082: 986: 952:Poisson distribution 868: 782: 735: 688: 631: 578: 567:Poisson distribution 389: 378:{\displaystyle \mu } 369: 318: 4916:normal distribution 4607:normal distribution 4561:is transcluding an 4559:Wakeby distribution 4403:normal distribution 4378:Normal Distribution 3862:Cantor distribution 3725:information entropy 3695:information entropy 3587: 3524:information entropy 3461: 2534:I definitely think 2354:Normal distribution 2337:Cantor distribution 2286:(multivariate Beta) 2251:normal distribution 2223:Landau distribution 2193:Cauchy distribution 2138:Pareto distribution 2068:Erlang distribution 1919:Zipf-Mandelbrot law 1604:User talk:MarkSweep 563:normal distribution 470:information entropy 258:Statistics articles 4983: 4918:we would include: 4901: 4789: 4686: 4605:For instance, the 4553:Error transclusion 4523:Hooman Mallahzadeh 4453:Gamma distribution 4337:(p.d.f.) and as a 3820:Exponential family 3813:Exponential family 3811:additional field? 3683: 3661: 3636: 3635: 3627: 3601: 3570: 3506: 3499: 3444: 3356: 3281:", for example. -- 3271: 3201: 3184: 3156: 3087: 3070: 3042: 3010: 2973: 2907: 2890: 2862: 2808: 2784: 2756: 2582:exponential family 2364:Gamma distribution 2268:Voigt distribution 2086:gamma distribution 1935:Gibbs distribution 1845:A - has an infobox 1528: 1474: 1441: 1436: 1432: 1416: 1285: 1228: 1212: 1114: 1056: 1040: 917:looks fine to me. 907: 888: 881: 829: 816: 809: 768: 755: 748: 721: 708: 701: 670: 651: 644: 617: 598: 591: 402: 375: 362:; brevity is key) 352: 190:Infoboxes articles 122:content assessment 92:dispute resolution 53: 4950: 4936: 4650: 4496: 4276:negative binomial 3905:less clashing? 3183: 3069: 3009: 2889: 2783: 2369:Beta distribution 2173:Wald distribution 2156:Rice distribution 2121:Lévy distribution 2015:beta distribution 1993:zeta distribution 1673:Beta distribution 1431: 1415: 1188: 1025: 426:"pdf" the pdf/pmf 274: 273: 270: 269: 266: 265: 202: 201: 198: 197: 102: 101: 72:Assume good faith 49: 16:(Redirected from 5036: 4992: 4990: 4989: 4984: 4982: 4981: 4971: 4966: 4951: 4943: 4938: 4937: 4929: 4910: 4908: 4907: 4902: 4897: 4896: 4872: 4871: 4798: 4796: 4795: 4790: 4788: 4784: 4780: 4775: 4774: 4765: 4764: 4729: 4728: 4704:has raw moments 4695: 4693: 4692: 4687: 4664: 4663: 4651: 4648: 4634: 4633: 4578: 4574: 4570: 4564: 4484: 4479: 4475: 4474: 4332: 4209:Hello everyone, 4114: 4110: 4107: 3692: 3690: 3689: 3684: 3645: 3643: 3642: 3637: 3586: 3581: 3554: 3553: 3515: 3513: 3512: 3507: 3460: 3455: 3365: 3363: 3362: 3357: 3334: 3280: 3278: 3277: 3272: 3255: 3210: 3208: 3207: 3202: 3185: 3181: 3165: 3163: 3162: 3157: 3096: 3094: 3093: 3088: 3071: 3067: 3051: 3049: 3048: 3043: 3011: 3007: 2982: 2980: 2979: 2974: 2916: 2914: 2913: 2908: 2891: 2887: 2871: 2869: 2868: 2863: 2817: 2815: 2814: 2809: 2804: 2803: 2785: 2781: 2765: 2763: 2762: 2757: 2752: 2751: 2056:chi distribution 1537: 1535: 1534: 1529: 1483: 1481: 1480: 1475: 1473: 1472: 1450: 1448: 1447: 1442: 1440: 1437: 1433: 1429: 1417: 1413: 1405: 1404: 1336: 1335: 1294: 1292: 1291: 1286: 1266: 1237: 1235: 1234: 1229: 1211: 1123: 1121: 1120: 1115: 1095: 1065: 1063: 1062: 1057: 1039: 916: 914: 913: 908: 886: 843:for an example). 838: 836: 835: 830: 814: 801: 777: 775: 774: 769: 753: 730: 728: 727: 722: 706: 679: 677: 676: 671: 649: 626: 624: 623: 618: 596: 411: 409: 408: 403: 401: 400: 384: 382: 381: 376: 361: 359: 358: 353: 348: 347: 260: 259: 256: 253: 250: 229: 222: 221: 211: 204: 192: 191: 188: 185: 182: 161: 154: 153: 143: 136: 113: 112: 111: 104: 27: 21: 5044: 5043: 5039: 5038: 5037: 5035: 5034: 5033: 5009: 5008: 4973: 4922: 4921: 4888: 4863: 4855: 4854: 4847: 4819: 4766: 4756: 4746: 4742: 4720: 4709: 4708: 4655: 4625: 4614: 4613: 4596: 4572: 4568: 4562: 4557:The infobox on 4555: 4539:199.169.204.151 4506: 4472: 4470: 4449: 4358: 4326: 4207: 4184: 4145: 4108: 4105: 4101: 4081: 4051: 4028: 4005: 3925: 3902: 3835: 3816: 3801: 3797: 3792: 3652: 3651: 3543: 3542: 3433: 3432: 3419: 3402: 3298: 3297: 3234: 3233: 3168: 3167: 3106: 3105: 3054: 3053: 2985: 2984: 2920: 2919: 2874: 2873: 2821: 2820: 2795: 2768: 2767: 2743: 2720: 2719: 2713: 2711:Italics or not? 2688: 2668: 2644: 2594:conjugate prior 2532: 2347: 1867: 1834: 1832:Status of usage 1599: 1502: 1501: 1464: 1459: 1458: 1435: 1434: 1425: 1419: 1418: 1409: 1390: 1370: 1327: 1322: 1321: 1251: 1250: 1138: 1137: 1080: 1079: 984: 983: 866: 865: 780: 779: 733: 732: 686: 685: 629: 628: 576: 575: 533: 514: 510: 495: 464:kurtosis excess 462:"kurtosis" the 456:"skewness" the 450:"variance" the 392: 387: 386: 367: 366: 339: 316: 315: 285: 279: 257: 254: 251: 248: 247: 189: 186: 183: 180: 179: 98: 97: 67: 23: 22: 15: 12: 11: 5: 5042: 5040: 5032: 5031: 5026: 5021: 5011: 5010: 4980: 4976: 4970: 4965: 4962: 4959: 4955: 4949: 4946: 4941: 4935: 4932: 4900: 4895: 4891: 4887: 4884: 4881: 4878: 4875: 4870: 4866: 4862: 4846: 4843: 4818: 4815: 4801: 4800: 4787: 4783: 4779: 4773: 4769: 4763: 4759: 4755: 4752: 4749: 4745: 4741: 4738: 4735: 4732: 4727: 4723: 4719: 4716: 4698: 4697: 4685: 4682: 4679: 4676: 4673: 4670: 4667: 4662: 4658: 4654: 4646: 4643: 4640: 4637: 4632: 4628: 4624: 4621: 4595: 4592: 4554: 4551: 4550: 4549: 4505: 4502: 4501: 4500: 4448: 4445: 4444: 4443: 4407: 4406: 4399: 4395: 4392: 4385: 4357: 4354: 4310:Best regards, 4306: 4304: 4303: 4298: 4293: 4288: 4283: 4278: 4273: 4268: 4263: 4261:hypergeometric 4258: 4253: 4248: 4243: 4238: 4233: 4228: 4223: 4206: 4203: 4183: 4180: 4179: 4178: 4144: 4141: 4140: 4139: 4138: 4137: 4119: 4118: 4080: 4077: 4050: 4047: 4027: 4024: 4004: 4001: 4000: 3999: 3998: 3997: 3935:for discrete ( 3924: 3921: 3901: 3898: 3897: 3896: 3895: 3894: 3834: 3831: 3815: 3809: 3799: 3795: 3791: 3788: 3787: 3786: 3785: 3784: 3783: 3782: 3768: 3752: 3682: 3679: 3676: 3673: 3670: 3667: 3664: 3659: 3648: 3647: 3646: 3633: 3630: 3625: 3622: 3619: 3616: 3613: 3610: 3607: 3604: 3599: 3596: 3593: 3590: 3585: 3580: 3577: 3573: 3569: 3566: 3563: 3560: 3557: 3552: 3534: 3533: 3519: 3518: 3517: 3516: 3505: 3502: 3497: 3494: 3491: 3488: 3485: 3482: 3479: 3476: 3473: 3470: 3467: 3464: 3459: 3454: 3451: 3447: 3443: 3440: 3427: 3426: 3418: 3415: 3401: 3398: 3397: 3396: 3395: 3394: 3393: 3392: 3372: 3371: 3370: 3369: 3368: 3367: 3355: 3352: 3349: 3346: 3343: 3340: 3337: 3333: 3330: 3327: 3324: 3321: 3318: 3315: 3312: 3308: 3305: 3289: 3288: 3287: 3286: 3270: 3267: 3264: 3261: 3258: 3254: 3251: 3248: 3245: 3242: 3227: 3226: 3212: 3211: 3200: 3197: 3194: 3191: 3188: 3178: 3175: 3155: 3152: 3149: 3146: 3143: 3140: 3137: 3134: 3131: 3128: 3125: 3122: 3119: 3116: 3113: 3098: 3097: 3086: 3083: 3080: 3077: 3074: 3064: 3061: 3041: 3038: 3035: 3032: 3029: 3026: 3023: 3020: 3017: 3014: 3004: 3001: 2998: 2995: 2992: 2972: 2969: 2966: 2963: 2960: 2957: 2954: 2951: 2948: 2945: 2942: 2939: 2936: 2933: 2930: 2927: 2917: 2906: 2903: 2900: 2897: 2894: 2884: 2881: 2861: 2858: 2855: 2852: 2849: 2846: 2843: 2840: 2837: 2834: 2831: 2828: 2818: 2807: 2802: 2798: 2794: 2791: 2788: 2778: 2775: 2755: 2750: 2746: 2742: 2739: 2736: 2733: 2730: 2727: 2712: 2709: 2708: 2707: 2687: 2684: 2683: 2682: 2677: 2667: 2664: 2662: 2643: 2640: 2639: 2638: 2637: 2636: 2625: 2624: 2623: 2622: 2615: 2614: 2602: 2601: 2579: 2577: 2576: 2575: 2574: 2560: 2559: 2531: 2528: 2527: 2526: 2525: 2524: 2523: 2522: 2521: 2520: 2519: 2518: 2502: 2501: 2500: 2499: 2498: 2497: 2496: 2495: 2473: 2472: 2471: 2470: 2469: 2468: 2455: 2454: 2453: 2452: 2442: 2441: 2440: 2439: 2432: 2431: 2430: 2429: 2423: 2422: 2418: 2417: 2408: 2407: 2406: 2405: 2404:distribution"? 2398: 2397: 2392: 2391: 2372: 2371: 2366: 2361: 2356: 2346: 2343: 2342: 2341: 2340: 2339: 2331: 2330: 2329: 2324: 2319: 2314: 2306: 2305: 2304: 2303: 2302: 2297: 2292: 2287: 2275: 2274: 2273: 2272: 2271: 2265: 2260: 2254: 2248: 2243: 2237: 2231: 2225: 2220: 2214: 2208: 2202: 2196: 2187: 2186: 2185: 2179: 2170: 2165: 2159: 2153: 2147: 2141: 2135: 2129: 2124: 2118: 2113: 2107: 2101: 2095: 2089: 2083: 2080:F-distribution 2077: 2071: 2065: 2059: 2050: 2049: 2048: 2042: 2036: 2030: 2024: 2018: 2012: 2000: 1999: 1998: 1997: 1996: 1990: 1984: 1978: 1972: 1966: 1960: 1954: 1953: 1952: 1947: 1942: 1937: 1924: 1923: 1922: 1916: 1910: 1904: 1898: 1892: 1886: 1880: 1866: 1863: 1859: 1858: 1855: 1852: 1849: 1846: 1833: 1830: 1814: 1813: 1805: 1801: 1793: 1792: 1791: 1790: 1789: 1788: 1787: 1786: 1769: 1768: 1767: 1766: 1765: 1764: 1751: 1750: 1749: 1748: 1738: 1737: 1736: 1735: 1720: 1719: 1718: 1717: 1710: 1709: 1700: 1699: 1694: 1693: 1690: 1689: 1688: 1685: 1677: 1676: 1668: 1667: 1660: 1659: 1652: 1651: 1650: 1649: 1638: 1637: 1598: 1595: 1586: 1585: 1584: 1564: 1552: 1551: 1547: 1546: 1541: 1540: 1527: 1524: 1521: 1518: 1515: 1512: 1509: 1490: 1489: 1471: 1467: 1454: 1453: 1452: 1451: 1439: 1426: 1424: 1421: 1420: 1410: 1408: 1403: 1400: 1397: 1393: 1389: 1386: 1383: 1380: 1377: 1376: 1373: 1369: 1366: 1363: 1360: 1357: 1354: 1351: 1348: 1345: 1342: 1339: 1334: 1330: 1316: 1315: 1284: 1281: 1278: 1275: 1272: 1269: 1265: 1261: 1258: 1239: 1238: 1227: 1224: 1221: 1218: 1215: 1210: 1207: 1204: 1201: 1198: 1195: 1191: 1187: 1184: 1181: 1178: 1175: 1172: 1169: 1166: 1163: 1160: 1157: 1154: 1151: 1148: 1145: 1130: 1129: 1113: 1110: 1107: 1104: 1101: 1098: 1094: 1090: 1087: 1068: 1067: 1066: 1055: 1052: 1049: 1046: 1043: 1038: 1035: 1032: 1028: 1024: 1021: 1018: 1015: 1012: 1009: 1006: 1003: 1000: 997: 994: 991: 965: 964: 947: 946: 931: 930: 906: 903: 900: 897: 894: 891: 885: 879: 876: 873: 862: 861: 845: 844: 828: 825: 822: 819: 813: 807: 804: 800: 797: 794: 791: 788: 767: 764: 761: 758: 752: 746: 743: 740: 720: 717: 714: 711: 705: 699: 696: 693: 669: 666: 663: 660: 657: 654: 648: 642: 639: 636: 616: 613: 610: 607: 604: 601: 595: 589: 586: 583: 571: 570: 550: 549: 532: 529: 528: 527: 518: 517: 512: 508: 494: 493:Standard Plots 491: 487: 486: 485: 484: 478: 472: 468:"entropy" the 466: 460: 454: 448: 442: 436: 430: 427: 424: 413: 399: 395: 374: 351: 346: 342: 338: 335: 332: 329: 326: 323: 308: 305: 302: 292: 283: 278: 275: 272: 271: 268: 267: 264: 263: 261: 244:the discussion 230: 218: 217: 212: 200: 199: 196: 195: 193: 176:the discussion 162: 150: 149: 144: 132: 131: 125: 114: 100: 99: 96: 95: 88: 83: 74: 68: 66: 65: 54: 45: 44: 41: 40: 39: 24: 14: 13: 10: 9: 6: 4: 3: 2: 5041: 5030: 5027: 5025: 5022: 5020: 5017: 5016: 5014: 5007: 5006: 5002: 4998: 4993: 4978: 4974: 4968: 4963: 4960: 4957: 4953: 4947: 4944: 4939: 4930: 4919: 4917: 4912: 4893: 4889: 4885: 4882: 4879: 4876: 4873: 4868: 4864: 4852: 4845:MLE estimates 4844: 4842: 4841: 4837: 4833: 4829: 4825: 4816: 4814: 4813: 4809: 4805: 4785: 4781: 4777: 4771: 4767: 4761: 4757: 4753: 4750: 4747: 4743: 4739: 4736: 4733: 4725: 4721: 4714: 4707: 4706: 4705: 4703: 4683: 4680: 4674: 4671: 4668: 4660: 4656: 4644: 4638: 4630: 4626: 4619: 4612: 4611: 4610: 4608: 4603: 4601: 4593: 4591: 4590: 4586: 4582: 4567: 4560: 4552: 4548: 4544: 4540: 4535: 4534: 4533: 4532: 4528: 4524: 4519: 4516: 4514: 4509: 4503: 4499: 4494: 4491: 4488: 4483: 4478: 4469: 4468: 4467: 4466: 4462: 4458: 4454: 4446: 4442: 4438: 4434: 4430: 4426: 4423: 4422: 4421: 4420: 4416: 4412: 4404: 4400: 4396: 4393: 4390: 4386: 4383: 4382: 4381: 4379: 4375: 4371: 4367: 4363: 4355: 4353: 4352: 4348: 4344: 4343:Michael Hardy 4340: 4336: 4330: 4324: 4323: 4319: 4315: 4311: 4308: 4302: 4299: 4297: 4294: 4292: 4289: 4287: 4284: 4282: 4279: 4277: 4274: 4272: 4269: 4267: 4264: 4262: 4259: 4257: 4254: 4252: 4249: 4247: 4244: 4242: 4239: 4237: 4234: 4232: 4229: 4227: 4224: 4222: 4219: 4218: 4217: 4214: 4210: 4204: 4202: 4201: 4197: 4193: 4189: 4181: 4177: 4173: 4169: 4165: 4164: 4163: 4162: 4158: 4154: 4150: 4142: 4136: 4132: 4128: 4123: 4122: 4121: 4120: 4117: 4112: 4111: 4098: 4097: 4096: 4095: 4091: 4087: 4078: 4076: 4075: 4071: 4067: 4062: 4059: 4055: 4048: 4046: 4045: 4041: 4037: 4032: 4025: 4023: 4022: 4018: 4014: 4009: 4002: 3996: 3992: 3988: 3984: 3980: 3976: 3972: 3971: 3969: 3965: 3961: 3957: 3954:Yes, and the 3953: 3952: 3951: 3950: 3946: 3942: 3938: 3934: 3930: 3929:math ref desk 3922: 3920: 3919: 3915: 3911: 3906: 3899: 3893: 3889: 3885: 3881: 3877: 3876: 3875: 3871: 3867: 3863: 3859: 3854: 3850: 3849: 3848: 3847: 3844: 3840: 3832: 3830: 3829: 3826: 3821: 3814: 3810: 3808: 3806: 3789: 3781: 3777: 3773: 3769: 3766: 3762: 3758: 3753: 3750: 3746: 3742: 3738: 3734: 3730: 3726: 3722: 3718: 3713: 3712: 3711: 3708: 3704: 3701: 3696: 3680: 3677: 3671: 3665: 3662: 3657: 3649: 3631: 3628: 3617: 3611: 3605: 3602: 3594: 3588: 3575: 3571: 3567: 3564: 3558: 3541: 3540: 3538: 3537: 3536: 3535: 3532: 3529: 3525: 3521: 3520: 3503: 3500: 3489: 3483: 3477: 3474: 3468: 3462: 3449: 3445: 3441: 3438: 3431: 3430: 3429: 3428: 3424: 3423: 3422: 3416: 3414: 3412: 3407: 3399: 3390: 3386: 3382: 3378: 3377: 3376: 3375: 3374: 3373: 3350: 3347: 3344: 3341: 3338: 3306: 3303: 3295: 3294: 3293: 3292: 3291: 3290: 3284: 3265: 3262: 3259: 3231: 3230: 3229: 3228: 3224: 3220: 3219: 3218: 3216: 3195: 3192: 3189: 3176: 3173: 3150: 3147: 3144: 3138: 3135: 3132: 3129: 3126: 3123: 3120: 3117: 3114: 3111: 3104: 3103: 3102: 3081: 3078: 3075: 3062: 3059: 3036: 3033: 3030: 3024: 3021: 3018: 3015: 3012: 3002: 2999: 2996: 2993: 2990: 2967: 2964: 2961: 2955: 2952: 2949: 2946: 2943: 2940: 2937: 2934: 2931: 2928: 2925: 2918: 2901: 2898: 2895: 2882: 2879: 2856: 2853: 2850: 2844: 2841: 2838: 2835: 2832: 2829: 2826: 2819: 2800: 2796: 2792: 2789: 2776: 2773: 2748: 2744: 2740: 2737: 2731: 2728: 2725: 2718: 2717: 2716: 2710: 2705: 2701: 2700: 2699: 2697: 2693: 2686:Inverse-gamma 2685: 2681: 2678: 2676: 2675:/link density 2673: 2672: 2671: 2665: 2663: 2660: 2659: 2656: 2652: 2650: 2641: 2634: 2629: 2628: 2627: 2626: 2619: 2618: 2617: 2616: 2612: 2608: 2605:Oh, and also 2604: 2603: 2599: 2595: 2591: 2590: 2589: 2587: 2583: 2572: 2568: 2564: 2563: 2562: 2561: 2557: 2553: 2552: 2551: 2549: 2545: 2541: 2537: 2529: 2516: 2512: 2511: 2510: 2509: 2508: 2507: 2506: 2505: 2504: 2503: 2493: 2489: 2485: 2481: 2480: 2479: 2478: 2477: 2476: 2475: 2474: 2466: 2461: 2460: 2459: 2458: 2457: 2456: 2450: 2446: 2445: 2444: 2443: 2436: 2435: 2434: 2433: 2427: 2426: 2425: 2424: 2420: 2419: 2415: 2410: 2409: 2402: 2401: 2400: 2399: 2394: 2393: 2389: 2384: 2383: 2382: 2380: 2375: 2370: 2367: 2365: 2362: 2360: 2357: 2355: 2352: 2351: 2350: 2344: 2338: 2335: 2334: 2332: 2328: 2325: 2323: 2320: 2318: 2315: 2313: 2310: 2309: 2307: 2301: 2298: 2296: 2293: 2291: 2288: 2285: 2282: 2281: 2279: 2278: 2276: 2269: 2266: 2264: 2261: 2258: 2255: 2252: 2249: 2247: 2244: 2241: 2238: 2235: 2232: 2229: 2226: 2224: 2221: 2218: 2215: 2212: 2209: 2206: 2203: 2200: 2197: 2194: 2191: 2190: 2188: 2183: 2180: 2178: 2174: 2171: 2169: 2166: 2163: 2160: 2157: 2154: 2151: 2148: 2145: 2142: 2139: 2136: 2133: 2130: 2128: 2125: 2122: 2119: 2117: 2114: 2111: 2108: 2105: 2102: 2099: 2096: 2093: 2090: 2087: 2084: 2081: 2078: 2075: 2072: 2069: 2066: 2063: 2060: 2057: 2054: 2053: 2051: 2046: 2043: 2040: 2037: 2034: 2031: 2028: 2025: 2022: 2019: 2016: 2013: 2010: 2007: 2006: 2004: 2003: 2001: 1994: 1991: 1988: 1985: 1982: 1979: 1976: 1973: 1970: 1967: 1964: 1961: 1958: 1955: 1951: 1948: 1946: 1943: 1941: 1938: 1936: 1933: 1932: 1931: 1928: 1927: 1925: 1920: 1917: 1914: 1911: 1908: 1905: 1902: 1899: 1896: 1893: 1890: 1887: 1884: 1881: 1878: 1875: 1874: 1872: 1871: 1869: 1868: 1864: 1862: 1856: 1853: 1850: 1847: 1844: 1843: 1842: 1839: 1831: 1829: 1828: 1824: 1820: 1811: 1806: 1802: 1799: 1795: 1794: 1785: 1782: 1777: 1776: 1775: 1774: 1773: 1772: 1771: 1770: 1762: 1757: 1756: 1755: 1754: 1753: 1752: 1746: 1742: 1741: 1740: 1739: 1732: 1728: 1724: 1723: 1722: 1721: 1714: 1713: 1712: 1711: 1707: 1702: 1701: 1696: 1695: 1691: 1686: 1682: 1681: 1679: 1678: 1674: 1670: 1669: 1665: 1662: 1661: 1657: 1654: 1653: 1647: 1642: 1641: 1640: 1639: 1635: 1632:scripting? -- 1631: 1626: 1622: 1621: 1620: 1618: 1613: 1608: 1607: 1605: 1596: 1594: 1592: 1582: 1578: 1574: 1573: 1572: 1570: 1563: 1561: 1556: 1549: 1548: 1543: 1542: 1522: 1519: 1516: 1510: 1507: 1499: 1498: 1497: 1493: 1487: 1469: 1465: 1456: 1455: 1422: 1414:for x=1,2,... 1406: 1401: 1398: 1395: 1387: 1384: 1381: 1371: 1367: 1361: 1358: 1355: 1349: 1346: 1340: 1332: 1328: 1320: 1319: 1318: 1317: 1313: 1312:0-534-24312-6 1310: 1306: 1302: 1301: 1300: 1298: 1279: 1276: 1273: 1259: 1256: 1248: 1244: 1225: 1219: 1213: 1205: 1196: 1193: 1189: 1185: 1176: 1167: 1164: 1155: 1149: 1143: 1136: 1135: 1134: 1127: 1108: 1105: 1102: 1088: 1085: 1077: 1073: 1069: 1053: 1047: 1041: 1036: 1033: 1030: 1026: 1022: 1016: 1013: 1010: 1001: 995: 989: 982: 981: 979: 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