Uniform Discrete Probability Distribution Family

A Uniform Discrete Probability Distribution Family is a discrete probability distribution family that is a uniform probability distribution family composed of uniform discrete probability functions.

• • …
• Counter-Example(s):
  • a Uniform Continuous Probability Distribution.
• See: Symmetric Distribution, Cumulative Distribution Function, Finite Support Discrete Probability Distribution Family.

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References

2015

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/Uniform_distribution_(discrete) Retrieved:2015-6-22.
  • In probability theory and statistics, the 'discrete uniform distribution is a symmetric probability distribution whereby a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n. Another way of saying "discrete uniform distribution" would be "a known, finite number of outcomes equally likely to happen".

    A simple example of the discrete uniform distribution is throwing a fair die. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of a given score is 1/6. If two dice are thrown and their values added, the resulting distribution is no longer uniform since not all sums have equal probability.

    The discrete uniform distribution itself is inherently non-parametric. It is convenient, however, to represent its values generally by an integer interval [a,b], so that a,b become the main parameters of the distribution (often one simply considers the interval [1,n] with the single parameter n). With these conventions, the cumulative distribution function (CDF) of the discrete uniform distribution can be expressed, for any k ∈ [a,b], as : [math]\displaystyle{ F(k;a,b)=\frac{\lfloor k \rfloor -a + 1}{b-a+1} }[/math]

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