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and not a factorial at all. This could cause confusion for people who aren't familiar with these functions/distributions. I propose altering the pdf formula to use a factorial function, which is mathematically appropriate because the parameter is always integral for the Erlang distribution. It is also more approachable to talk about factorials than the gamma function, which is rather elaborately defined. For an integer k, it is always the case that Gamma(k) = (k-1)!.
22:
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It is worth pointing out the need for at least a minor correction. Under "Properties" if indeed the denominator is gamma(k) then since that is (k-1)! then saying that is the
Poisson Distribution is incorrect, since the denominator for the Poisson Distribution is k!, not (k-1)!. (Observation by ecsd
643:
In the section "Probability density function" the article currently says that the gamma is a generalization using the gamma function instead of the factorial function. While this is true in a very real sense, the formula we provided for the Erlang already uses the gamma function in its denominator,
519:
I've found this page to be useful. More useful than the page on the Gamma distribution. One thing I like about this page is that it is explained, in simple terms, where the Erlang distribution comes from. It is relatively easy to understand, since, in part 'k' is an integer (event number). But the
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The redirect from the Erlang-B page, via the Erlang-C reference link, is completely incorrect. As already noted several times, this page presents the Erlang_k or restricted Gamma distribution. The B and C functions are usually treated separately from the the k-distribution because they arise in an
507:
The Erlang is widely used and named as its own distribution. It deserves a page of its own with explicit reference to the Gamma. Algebraically, it is often possible to generate
Erlangs in computer programs where it would much harder to generate Gammas since the factorial is widely defined but the
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this article should be kept, since Erlang is also used in domains that are less familiar with the general gamma distribution. Isn't \lambda the same as the standard deviation - a term less used in formal statistics but still used in other domains. What is its relationship to the
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plots would work just as well, if only the two articles agreed on whether to use θ or λ as the parameter. It would also facilitate understanding the relationship between the two distributions. Is there any reason not to choose one and have both articles use the same parameter?
611:
The Erlang-B and Erlang-C formulae are queue theory results giving the discrete probability distributions of the numbers in steady-state queues with certain characteristics (blocked -customers-cleared, for example). They are not usually referred to as Erlang
Distributions.
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Erlang
Distribution is a continuous distribution, a special case of the gamma but with some special characeristics - it can be modelled as a sum of exponentials, for example. I think that it unique enough that it should have its own page as well as being referred to in the
703:
I think that, "the waiting times between k occurrences of the event are Erlang distributed," should be changed to "the waiting time until the kth occurrence of the event," which I would say is equivalent to "the waiting time between k+1 occurrences of the event".
386:
The expression for the entropy of the erlang distribution is probably wrong. Consider the case of k=1 where the erlang reduces to a simple exponential distribution whose entropy is (1- ln (lambda)). The expression provided reduces to 1/lambda.
520:
meaning of the Gamma distribution, for which the corresponding parameter is real, is a mystery to me. I say keep this page, but fix the Gamma distribution page, which is lacking any kind of motivational explanation.
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There may be a reason. If I remember correctly when you do the math to derive the erlang from the exponential, you get one parameter. Then, the Gamma generally uses the other. I'll look into it.
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There is no such thing as a cumulative DENSITY function. The letters "CDF" stand for "cumulative distribution function". The words "cumulative" and "density" contradict each other.
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The discussions on this page have been reogranized. I have split previous comments up and duplicated the signature lines when spliting comments and added braces for clarity.
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I assume the posted formula for the cdf is over a range from 0 to x. Is this correct? I've found this integral difficult to perform, hence my question.
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The two equivalent formulations of the
Probability density function are so trivially equivalent that one of them should be deleted.
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I added plots from the Gamma distribution article, but the CDF does not appear in my browser. Does it look ok to everyone else?
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630:{t}The Erlang-B and Erlang-C formulae are mentioned in the Erlang Unit page. I will modify this page when I have time. --
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603:{However, w}{W}hat exactly do you mean by Erlang formulae vs. Erlang distribution? Would you care to elaborate? --
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471:(unless it can be significantly expanded to include a detailed discussion of the phone traffic scenario). --
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The material on the Erlang
Formulae should be moved to another page-- it is not the Erlang Distributiion.
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881:. Either the variable names in the legends or the variable names in the text need to be changed.
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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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Ok, then the present article should be kept and revised to reflect the situation you describe. --
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Ok, then the present article should be kept and revised to reflect the situation you describe. --
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entirely different context in queueing theory. The correct content for Erlang-C exists at
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Please define the constants in the equation. I would but I don't know what they are!
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We do not need a long article here since the Erlang distribution is basically the
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The explanation of the waiting time interpretation uses imprecise language
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It is true that they are all actually probability distributions but
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The
Cumulative Density Function is wrong. It should be 1 - ...
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302:{\displaystyle \scriptstyle {\frac {1}{k}}(\lambda \,-\,1)\,}
213:{\displaystyle \scriptstyle {\frac {1}{\lambda }}(k\,-\,1)\,}
426:. Unfortunately, it's in German but the math is correct.
343:(not sure if the constraint should be changed or not).
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More specific definition of cumulative would be welcome
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336:{\displaystyle \scriptstyle l\;\geq \;1\,}
247:{\displaystyle \scriptstyle k\;\geq \;1\,}
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38:It is of interest to the following
917:Low-importance Statistics articles
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751:sorry, I just couldn't find them.
740:. Am I missing something here? --
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99:Knowledge:WikiProject Statistics
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897:14:57, 16 November 2021 (UTC)
831:18:43, 23 February 2019 (UTC)
782:18:09, 10 November 2010 (UTC)
93:and see a list of open tasks.
762:Probability density function
446:22:15, 2 February 2008 (UTC)
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788:Cumulative Density Function
570:21:53, 21 August 2005 (UTC)
565:Looks great to me, thanks.
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402:22:52, 8 January 2009 (UTC)
359:06:48, 13 August 2012 (UTC)
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808:11:38, 22 April 2016 (UTC)
665:14:36, 31 March 2014 (UTC)
580:You should better explain
489:page as a special case. --
463:I agree that this article
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157:19:54, 7 March 2014 (UTC)
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366:Fixed Entropy Expression
163:Mode is wrong (99% sure)
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