The negative binomial distribution
Kaller, Cecil Louis
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Recent studies on biological data which vary somewhat from Poisson description have brought the negative binomial distribution into greater prominence. Data such as accident statistics and insect counts, in which relatively complex factors are at work, lend themselves to negative binomial description. In sampling from negative binomial populations there is the problem of fitting the distribution function (q - p)-k to the data. This involves the simulaaneous estimation of the two parameters p and k. Several methods are described by which this may be done and the efficiencies of these methods are discussed. Two techniques fortesting the adequacy of the fit obtained by these estimation methods are described. The pooling or Poisson sub-samples wherein means are distributed according to the Pearson Type III function is described by the negative binomial distribution. This compounding is discussed with some analysis of variance techniques and notes on the significance of such compound samples. The problem of pooling negative binomial sub-samples remains to be investigated. Papers are available discussing the applications of confidence interval theory to the parameters of distributions such as the binomial, normal, and Poisson, all related to the negative binomial. Techniques are devised in this thesis for applying confidence interval concepts to the negative binomial parameters for a selected range of parameter values. Included are confidence belt charts with a discussion of their use.