Statistical models of biased sampling of two non-central hypergeometric distributions Wallenius' and Fisher's distribution has been extensively used in the literature, however, not many of the logic of hypergeometric distribution have been investigated by different techniques. This research work examined the procedure of the two non-central hypergeometric distributions and investigates the statistical properties which includes the mean and variance that were obtained. The parameters of the distribution were estimated using the direct inversion method of hyper simulation of biased urn model in the environment of R statistical software, with varying odd ratios (w) and group sizes (mi). It was discovered that the two non - central hypergeometric are approximately equal in mean, variance and coefficient of variation and differ as odds ratios (w) becomes higher and differ from the central hypergeometric distribution with ω = 1. Furthermore, in univariate situation we observed that Fisher distribution at (ω = 0.2, 0.5, 0.7, 0.9) is more consistent than Wallenius distribution, although central hypergeometric is more consistent than any of them. Also, in multinomial situation, it was observed that Fisher distribution is more consistent at (ω = 0.2, 0.5), Wallenius distribution at (ω = 0.7, 0.9) and central hypergeometric at (ω = 0.2)
A Bayesian solution to the Behrens–Fisher problem
