This thesis is an extensive review of the major literature dealing with the negative binomial distribution. An account of the forms of the distribution is presented. This includes compound, limiting and truncated forms and examples of their occurrence. Parameter estimation is treated in a few specific cases.

In particular, the inverse binomial sampling form, its analytic properties, occurrence in biological as well as industrial situations, estimation of the parameter p, and hypothesis testing are discussed in detail. Many examples are included.

In the discussion of the inverse binomial sampling form several extremely useful, little known relations are presented. Among these is a discussion of the use of the Tables of the Incomplete Beta Function for the evaluation of the cumulative distribution function. Also discussed is the method of adapting Biometrika Table 41, which gives confidence limits on p in the positive binomial case, to the inverse binomial sampling case.