Generalized endpoint-inflated binomial model

To model binomial data with large frequencies of both zeros and right-endpoints, Deng and Zhang (in press) recently extended the zero-inflated binomial distribution to an endpoint-inflated binomial (EIB) distribution. Although they proposed the EIB mixed regression model, the major goal of Deng and Zhang (2015) is just to develop score tests for testing whether endpoint-inflation exists. However, the distributional properties of the EIB have not been explored, and other statistical inference methods for parameters of interest were not developed. In this paper, we first construct six different but equivalent stochastic representations for the EIB random variable and then extensively study the important distributional properties. Maximum likelihood estimates of parameters are obtained by both the Fisher scoring and expectation-maximization algorithms in the model without covariates. Bootstrap confidence intervals of parameters are also provided. Generalized and fixed EIB regression models are proposed and the corresponding computational procedures are introduced. A real data set is analyzed and simulations are conducted to evaluate the performance of the proposed methods. All technical details are put in a supplemental document (see Appendix A).