Probability Distributions

Probability Distributions (or just distributions) is an omnibus phrase covering frequency functions, probability functions, probability mass functions, probability densities, density functions and densities. It is not synonymous with distribution functions nor cumulative distribution functions, F(x). The word common needs some comment. The thirty or so distributions included in this booklet, though varying somewhat in sophistication, are believed to be the most common ones. It would have been possible to add other distributions such as the circular Normal distribution, the Inverse Gaussian distribution, the truncated Poisson distributions or mixtures. Instead, some blank pages are included at the end for such additions, should their need arise. The distributions described in this booklet are mathematical models. In practice, however, one is almost invariably concerned with samples whose size may be quite small, with concomitant sampling errors as well as those which automatically occur when measurements are made. A small table of such measurements is given in Appendix 2, together with the associated histogram and the theoretical distribution appropriate to the histogram.
What has been said above applies to many, but not all, of the theoretical distributions described in this booklet. No knowledge of calculus is required to read this booklet because the small number of places where it is needed can, if necessary, be ignored.