Talk:Discrete uniform distribution

Untitled

EDITORS! Please see Wikipedia:WikiProject Probability#Standards for a discussion of standards used for probability distribution articles such as this one.

--- — Preceding unsigned comment added by MLópez-Ibáñez (talk • contribs) 13:39, 10 October 2012 (UTC)

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.

Also, the statement that "The convention is used that the cumulative mass function Fk(ki) is the probability that k > = ki" seems mistaken, the correct version being "The convention is used that the cumulative mass function Fk(ki) is the probability that k < = ki". —Preceding unsigned comment added by 129.67.96.122 (talk) 05:37, 11 March 2006 (UTC)

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Could someone explain to me if in the graph the lines should be dotted or not? (KMF) —Preceding unsigned comment added by 88.107.210.122 (talk) 23:31, 28 May 2006 (UTC)

Unclear

Can anyone expand on "compare ${\frac {m}{k}}$ above"? What was the point being made? Melcombe (talk) 17:00, 19 February 2009 (UTC)

Mean and Variance

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. —Preceding unsigned comment added by Beefpelican (talk • contribs) 14:33, 16 November 2009 (UTC)

Also unclear

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"

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..."

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. —Preceding unsigned comment added by 207.22.18.83 (talk) 14:25, 11 April 2010 (UTC)

Random?

The plots on the right use equidistant numbers, not the thing one would expect from random numbers. — Preceding unsigned comment added by Muhali (talk • contribs) 17:37, 18 January 2013 (UTC)

Printing issues

I'm wondering why the 'Notation' and 'Parameters' parts don't print as they appear on the page; everything else prints OK.

71.139.162.77 (talk) 05:45, 22 October 2014 (UTC)

Distribution of sums of discrete uniform random variables

Mathworld.Wolfram (http://mathworld.wolfram.com/Dice.html) describes the distributions which arise from the sum of dice rolls. I feel as if the information needs to be condensed and transferred in a copyright respecting format.

Here is my take at deriving the distribution of independent sums of discrete uniform random variables:
For $n$ s-sided dice each independent and $\sim {\mathcal {U}}(1,s)$, summing over each additional die performs discrete convolution
$pmf(k,n,s)=\sum _{i=1}^{s}pmf(k,n-1,s)*p(k-i={\mathcal {U}}(1,s))$
$pmf(k,1,s)={\begin{cases}1/s&{\textrm {if}}1\leq k\leq s\\0&{\textrm {otherwise}}\end{cases}}$
Then it is a straightforward case of induction to show that pmf described on http://mathworld.wolfram.com/Dice.html fulfills the above recursion (assuming I avoided making mistakes).Mouse7mouse9 04:28, 24 February 2015 (UTC)

Suspect intuitive interpretation

The section Estimation of maximum says

The UMVU estimator for the maximum is given by

${\hat {N}}={\frac {k+1}{k}}m-1=m+{\frac {m}{k}}-1$

where m is the sample maximum and k is the sample size, sampling without replacement. This can be seen as a very simple case of maximum spacing estimation.

The formula may be understood intuitively as

the sample maximum plus the average gap between observations in the sample,

the gap being added to compensate for the negative bias of the sample maximum as an estimator for the population maximum. [Note: The sample maximum is never more than the population maximum, but can be less, hence it is a biased estimator: it will tend to underestimate the population maximum.]

This intuition seems wrong to me, by this counterexample: Say our observations are {1,4}. The formula gives ${\hat {N}}$ = 4 + 4/2 – 1 = 5. But the suggested intuition gives 4 + 3 =7.

Am I missing something, or is the stated intuitive interpretation wrong? Loraof (talk) 22:55, 3 June 2017 (UTC)

يقاف الجهزه

انهاتشكل خطر علجهاز 37.237.64.30 (talk) 00:06, 9 February 2024 (UTC)