Finite Support Discrete Probability Distribution Family

A Finite Support Discrete Probability Distribution Family is a discrete probability distribution family with finite support.

• Context:
  • …
• Example(s):
  • Rademacher Distribution.
  • Binomial Distribution, such as a Bernoulli distribution.
  • Beta-Binomial Model.
  • Degenerate Distribution.
  • Uniform Distribution (Discrete).
  • Hypergeometric Distribution.
  • Poisson Binomial Distribution.
  • Fisher's Noncentral Hypergeometric Distribution.
  • Wallenius' Noncentral Hypergeometric Distribution.
• Counter-Example(s):
  • a Discrete/Continuous Probability Distribution Family.
  • a Continuous Probability Distribution Family.
• See: Statistical Model Family, Probability Model Fitting, Benford's Law.

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References

2014

• (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/List_of_probability_distributions#With_finite Retrieved:2014-10-28.
  • • The Bernoulli distribution, which takes value 1 with probability p and value 0 with probability q = 1 − p.
    • The Rademacher distribution, which takes value 1 with probability 1/2 and value −1 with probability 1/2.
    • The binomial distribution, which describes the number of successes in a series of independent Yes/No experiments all with the same probability of success.
    • The beta-binomial distribution, which describes the number of successes in a series of independent Yes/No experiments with heterogeneity in the success probability.
    • The degenerate distribution at x₀, where X is certain to take the value x₀. This does not look random, but it satisfies the definition of random variable. This is useful because it puts deterministic variables and random variables in the same formalism.
    • The discrete uniform distribution, where all elements of a finite set are equally likely. This is the theoretical distribution model for a balanced coin, an unbiased die, a casino roulette, or the first card of a well-shuffled deck.
    • The hypergeometric distribution, which describes the number of successes in the first m of a series of n consecutive Yes/No experiments, if the total number of successes is known. This distribution arises when there is no replacement.
    • The Poisson binomial distribution, which describes the number of successes in a series of independent Yes/No experiments with different success probabilities.
    • Fisher's noncentral hypergeometric distribution.
    • Wallenius' noncentral hypergeometric distribution.
    • Benford's law, which describes the frequency of the first digit of many naturally occurring data.

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