Introduction

Many different shapes of discrete distribution can be obtained by varying the parameters R, B and n in the hypergeometric distribution (section 10.13). When, for example, R = B and both are very large, and a reasonably large random sample of size n is drawn, the distribution of the number of red objects chosen is effectively binomial with parameters n (large) and p = ½. We then have a symmetric discrete distribution closely resembling the normal. By varying the hypergeometric parameters, we are able to produce distributions with different levels of skewness and kurtosis (section 8.6). Karl Pearson observed this, and he devised the Pearson system of probability-density functions by using a differential equation similar to the difference equation of the discrete hypergeometric distribution.

The process of fitting a Pearson probability-density function usually involves a large amount of arithmetic, but the work is nowhere near as onerous as previously now that electronic desk calculators are available with exponential, logarithmic and trigonometric keys.