Talk:Discrete uniform distribution

Untitled
EDITORS! Please see WikiProject Probability 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)

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)