Fisher's Noncentral Hypergeometric Distribution
In the Fisher model, the fates of the balls are independent and there is no dependence between draws. We may as well take all n balls at the same time. Each ball has no "knowledge" of what happens to the other balls. For the same reason, it is impossible to know the value of n before the experiment. If we tried to fix the value of n then we would have no way of preventing ball number n+1 from being taken without violating the principle of independence between balls. n is therefore a random variable, and the Fisher distribution is a conditional distribution which can only be determined after the experiment when n is known. The unconditional distribution is two independent binomials, one for each color.
Fisher's distribution can simply be defined as the conditional distribution of two or more independent binomial variates dependent upon their sum. A multivariate version of the Fisher's distribution is used if there are more than two colors of balls.
Read more about this topic: Noncentral Hypergeometric Distributions
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