2008/02/01 by Agner Fog · 2 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Statistical Methods and Bayesian Inference #Statistical Distribution Estimation and Applications #Hypergeometric distribution #Mathematics #Noncentral chi-squared distribution #Confluent hypergeometric function #Applied mathematics #Hypergeometric function #Binomial distribution #Mathematical analysis #Statistics #Ratio distribution #Asymptotic distribution
paper · doi:10.1080/03610910701790269
openalex publication_date 2008/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
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.