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2) Since this is an expansion of the original thought to real-valued discrete variables, perhaps the original (simpler) thought should just be continued; ie - put this paragraph further down the article after the discussion about integer values has been more fully developed.
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There's quite a lot in this article that I would not buy into. The restriction that parameters and points of support be integers is not necessary. Rather, n equally likely events can be inscribed into any interval, and the formula n=b-a+1 then no longer holds.
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Note the paragraph at top which reads: "In case the values of a random variable with a discrete uniform distribution are real, it is possible to express the cumulative distribution function in terms of the degenerate distribution; thus"
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1) I believe I know what it's trying to say, but it's wildly ambiguous. A simple syntactic rewrite would make this much clearer, as in "When a random variable has discrete values which are not integers..."
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Shouldn't both of these be the sum of ni/n, (that is, the sum of the point values divided by the number of points)? (a+b)/2 only works if you have a discrete uniform distribution with only two points.
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301:= ki" seems mistaken, the correct version being "The convention is used that the cumulative mass function Fk(ki) is the probability that k < = ki".
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I'm wondering why the 'Notation' and 'Parameters' parts don't print as they appear on the page; everything else prints OK.
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the gap being added to compensate for the negative bias of the sample maximum as an estimator for the population maximum.
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Also, the statement that "The convention is used that the cumulative mass function Fk(ki) is the probability that k : -->
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850:{\displaystyle pmf(k,1,s)={\begin{cases}1/s&{\textrm {if}}1\leq k\leq s\\0&{\textrm {otherwise}}\end{cases}}}
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fulfills the above recursion (assuming I avoided making mistakes).Mouse7mouse9 04:28, 24 February 2015 (UTC)
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This intuition seems wrong to me, by this counterexample: Say our observations are {1,4}. The formula gives
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Here is my take at deriving the distribution of independent sums of discrete uniform random variables:
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The plots on the right use equidistant numbers, not the thing one would expect from random numbers.
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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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for a discussion of standards used for probability distribution articles such as this one.
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Could someone explain to me if in the graph the lines should be dotted or not? (KMF)
734:{\displaystyle pmf(k,n,s)=\sum _{i=1}^{s}pmf(k,n-1,s)*p(k-i={\mathcal {U}}(1,s))}
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Then it is a straightforward case of induction to show that pmf described on
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the sample maximum plus the average gap between observations in the sample
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Am I missing something, or is the stated intuitive interpretation wrong?
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961:{\displaystyle {\hat {N}}={\frac {k+1}{k}}m-1=m+{\frac {m}{k}}-1}
1041:= 4 + 4/2 â 1 = 5. But the suggested intuition gives 4 + 3 =7.
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Distribution of sums of discrete uniform random variables
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