Inference on Two-Parameter Negative Binomial Distributions: One- and Two-Sample Problems

Music City Center 

A modified likelihood ratio test and confidence intervals for the mean of a two-parameter negative binomial (NB) distribution are proposed and compared with available ones. The problems of testing/estimating the ratio or the difference of the means of two NB distributions are also considered.
Assuming that the dispersion parameters are equal an improved version of the likelihood ratio test for the ratio of means of two NB distributions is proposed. Methods of variance estimate recovery (MOVER) are used to find confidence intervals for the ratio or the difference of two means when the dispersion parameters are unknown and arbitrary. The tests and interval estimation methods are illustrated using an example with count data on seizures from two groups of patients.

over-dispersion

powers

score test

standardized LRT

type I error 

Section on Statistical Computing