Two New Bivariate Zero-Inflated Generalized Poisson Distributions with a Flexible Correlation Structure

• Activity Number: 82
• Type: Contributed
• Date/Time: Sunday, August 9, 2015 : 4:00 PM to 5:50 PM
• Sponsor: Biometrics Section
• Author(s): CHI Zhang*
• Keywords: Bivariate generalized Poisson distribution ; Expectation-maximization algorithm ; Newton-Raphson algorithm ; Over-dispersion ; Zero-inflated generalized Poisson distribution

Abstract

To model correlated bivariate count data with extra zero observations, this paper proposes two new bivariate zero-inflated generalized Poisson (ZIGP) distributions by incorporating a multiplicative factor (or dependency parameter) ?, named as Type I and Type II bivariate ZIGP(?) distributions, respectively. The proposed distributions possess a flexible correlation structure and can be used to fit either positively or negatively correlated and either over- or under-dispersed count data, comparing to the existing models that can only fit positively correlated count data with over-dispersion. The two marginal distributions share a common parameter of zero inflation in Type I bivariate ZIGP(?) while have their own parameters of zero inflation in Type II bivariate ZIGP(?), resulting in a much wider range of applications. The important distributional properties are explored and some useful statistical inference methods including MLE of parameters, bootstrap confidence intervals and related testing hypotheses are developed. A real data are thoroughly analyzed by using the proposed distributions. Several simulation studies are conducted to evaluate the performance of the proposed methods.