A generalized negative binomial (GNB) distribution with an additional parameter β has been obtained by using Lagrange's expansion. The parameter is such that both mean and variance tend to increase or ...

For binomial and Poisson distributions, the scale parameter has a value of 1. The variance of Y is for the binomial distribution and for the Poisson distribution. Overdispersion occurs when the ...

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Using the C(α) procedure of Neyman (1959), we derive tests for the goodness of fit of the binomial distribution which are asymptotically optimal against generalized binomial alternatives proposed by ...