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
Famous quotes containing the words fisher and/or distribution:
“A mother is not a person to lean on but a person to make leaning unnecessary.”
—Dorothy Canfield Fisher (20th century)
“The man who pretends that the distribution of income in this country reflects the distribution of ability or character is an ignoramus. The man who says that it could by any possible political device be made to do so is an unpractical visionary. But the man who says that it ought to do so is something worse than an ignoramous and more disastrous than a visionary: he is, in the profoundest Scriptural sense of the word, a fool.”
—George Bernard Shaw (1856–1950)