Title: Zero-truncated poisson-power function distribution

Abstract

Construction of flexible distributions for improved modeling of complex real-life data is currently receiving a widespread attention by statisticians and researchers in other disciplines. In this paper, we introduce and study a new distribution called the zero-truncated Poisson-power function distribution (ZTPPFD). The ZTPPFD was obtained by compounding the zero-truncated Poisson distribution and the power function distribution. The asymptotic, shape properties, and other mathematical properties of the distribution were studied. Moreover, the power function distribution is identified as the limiting case of the ZTPPFD when the only parameter λ of the zero-truncated Poisson distribution approaches zero. However, the hazard rate function of the new distribution is found to contain some important shapes of the hazard rate of some lifetime phenomena that are commonly encountered in practice, they are increasing, bathtub , and upside-down bathtub shapes. Estimation of the distribution parameters was carried out by the method of maximum likelihood and a numerical study show that the maximum likelihood estimation method provides good estimates of the distribution parameters. Two examples are presented to illustrate the usefulness and fitting performance of the ZTPPFD in modeling complex real data-sets. The ZTPPFD can be applied in other areas such as demography, reliability engineering, meteorology, and hydrology.