Simultaneous estimators of the dispersion parameters in m negative binomial distributions with known success probabilities are shown to dominate the usual estimator under squared error loss by shrinking it toward either a fixed or a data-driven point.

Homogeneity of dispersion parameters is a standard assumption in inverse Gaussian regression analysis. However, this assumption is not necessarily appropriate. This paper is devoted to the test for varying dispersion in general inverse Gaussian linear regression models. Based on the modified...