Inference for Zero Inflated Truncated Power Series Family of Distributions

Zero-inflated data indicates that the data set contains an excessive number of zeros. The word zero-inflation is used to emphasize that the probability mass at the point zero exceeds than the one allowed under a standard parametric family of discrete distributions. Gupta et al. [1], Murat & Szynal [2], Patil & Shirke [3] have contributed to estimation and testing of the parameters involved in Zero Inflated Power Series Distributions. If the data set under study does not contain observations after some known point in the support, we have to modify Zero Inflated Power Series Distribution (ZIPSD) accordingly in order to get better inferential properties. Zero Inflated Truncated Power Series Distribution (ZITPSD) is one of the better options. In the present work we address problem of estimation for ZITPSD with more emphasis on statistical tests. We provide three asymptotic tests for testing the parameter of ZITPSD, using an unconditional (standard) likelihood approach, a conditional likelihood approach and the sample mean, respectively. The performance of first two tests has been studied for Zero Inflated Truncated Poisson Distribution (ZITPD). Asymptotic Confidence Intervals for the parameter are also provided. The model has been applied to a real life data.