Testing for Homogeneity of k Independent Negative Binomial Distributed Random Variables.

In this article the problem of testing for homogeneity of k (k > 3) independent negative binomial distributed random variables with parameters r[sub i], p (for i = 1, ..., k) is studied. The alternative hypotheses which are considered are a p-mixture of negative binomial distributions and a positive trend of the p's. Several cases may be distinguished: (1)p known, (2) p unknown and r[sub 1] =...= r[sub k],(3)p unknown and r[sub 1], ..., r[sub kappa] possibly unequal. The proposed tests are based on explicit optimality criteria. [ABSTRACT FROM AUTHOR]