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The test based on the hypergeometric distribution (hypergeometric test) is identical to the corresponding one-tailed version of Fisher's exact test. [6] Reciprocally, the p-value of a two-sided Fisher's exact test can be calculated as the sum of two appropriate hypergeometric tests (for more information see [7]).
The probability distribution of employed versus unemployed respondents in a sample of n respondents can be described as a noncentral hypergeometric distribution. The description of biased urn models is complicated by the fact that there is more than one noncentral hypergeometric distribution. Which distribution one gets depends on whether items ...
Probability mass function for Wallenius' Noncentral Hypergeometric Distribution for different values of the odds ratio ω. m 1 = 80, m 2 = 60, n = 100, ω = 0.1 ... 20. In probability theory and statistics, Wallenius' noncentral hypergeometric distribution (named after Kenneth Ted Wallenius) is a generalization of the hypergeometric distribution where items are sampled with bias.
The bias or odds can be estimated from an experimental value of the mean. Use Wallenius' noncentral hypergeometric distribution instead if items are sampled one by one with competition. Fisher's noncentral hypergeometric distribution is used mostly for tests in contingency tables where a conditional distribution for fixed margins is desired ...
Unlike the standard hypergeometric distribution, which describes the number of successes in a fixed sample size, in the negative hypergeometric distribution, samples are drawn until failures have been found, and the distribution describes the probability of finding successes in such a sample.
The probability distribution of the sum of two or more independent random variables is the convolution of their individual distributions. The term is motivated by the fact that the probability mass function or probability density function of a sum of independent random variables is the convolution of their corresponding probability mass functions or probability density functions respectively.
Hypergeometric function lists identities for the Gaussian hypergeometric function; Generalized hypergeometric function lists identities for more general hypergeometric functions; Bailey's list is a list of the hypergeometric function identities in Bailey (1935) given by Koepf (1995). Wilf–Zeilberger pair is a method for proving hypergeometric ...
If p = 1/n and X is geometrically distributed with parameter p, then the distribution of X/n approaches an exponential distribution with expected value 1 as n → ∞, since (/ >) = (>) = = = [()] [] =. More generally, if p = λ/n, where λ is a parameter, then as n→ ∞ the distribution of X/n approaches an exponential distribution with rate ...