Journal
COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION
Volume 37, Issue 2, Pages 258-273Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/03610910701790269
Keywords
biased sampling; natural selection; Wallenius noncentral hypergeometric distribution
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Two different probability distributions are both known in the literature as the noncentral hypergeometric distribution. Wallenius' noncentral hypergeometric distribution can be described by an urn model without replacement with bias. Fisher's noncentral hypergeometric distribution is the conditional distribution of independent binomial variates given their sum. No reliable calculation method for Wallenius' noncentral hypergeometric distribution has hitherto been described in the literature. Several new methods for calculating probabilities from Wallenius' noncentral hypergeometric distribution are derived. Range of applicability, numerical problems, and efficiency are discussed for each method. Approximations to the mean and variance are also discussed. This distribution has important applications in models of biased sampling and in models of evolutionary systems.
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