DefinePK

Abstract

This paper introduces and investigates a new one-parameter zero-inflated count distribution. The new model is named the zero-inflated Poisson XLindley (ZIPXL) distribution. The fundamental mathematical characteristics of the ZIPXL model - including survival analysis, hazard function, generating functions, moments (mean and variance), dispersion index, skewness coefficient, kurtosis, and order statistics—are derived. Maximum likelihood is used to estimate the parameters of the ZIPXL distribution. An intensive simulation study is conducted to assess the performance of these estimators. The research demonstrates the practical utility and flexibility of the new distribution in managing excess zero data in real-world applications, using two real-world datasets from the medical field. The research compares the ZIPXL distribution with the zero-inflated Poisson moment exponential distribution and the zero-inflated Poisson distribution. Provides evidence that the ZIPXL distribution performs effectively in examining overdispersed count data.