EXTENDED PSEUDO-LINDLEY POISSON DISTRIBUTION: A NEW MODEL FOR COUNT DATA WITH APPLICATION TO VIRULENT TUBERCLE BACILLI DATA

Abstract

This paper introduces a new lifetime probability distribution called the Extended Pseudo-Lindley-Poisson Distribution (EPLPD), which generalizes the Pseudo-Lindley Distribution and the Poisson Distribution. The EPLPD is designed to model count data with varying degrees of dispersion, including zero-inflation and over dispersion. We derive the properties of the EPLPD, including its probability mass function, cumulative distribution function, moments, and moment generating function The maximum likelihood estimation method is used to estimate the parameters of the EPLPD. To demonstrate the applicability of the EPLPD, a numerical example was the survival times (in days) of 72 Guinea pigs infected with virulent tubercle bacilli is presented, demonstrating the distribution's superiority over existing models. The results show that the EPLPD provides a better fit to the data compared to the Poisson and Lindley distributions. The EPLPD can be used to model various types of count data in fields such as medicine, biology, and engineering. The EPLPD offers a valuable tool for analyzing count data in various fields, including medicine, biology, and public health