A New Flexible Distribution Based on the Zero Truncated Poisson Distribution: Mathematical Properties and Applications to Lifetime Data

Abstract

The so called zero truncated Poisson (ZTP) distribution is a discrete probability model whose support is the set of only the positive integers ( ) + I . The ZTP is also known as the positive Poisson distribution or the conditional Poisson distribution. It is the conditional probability distribution of a Poisson-distributed random variable (RV), given that the value of the RV is 0. ≠ Thus, it is impossible for a ZTP RV to be zero, in this paper we will introduce a new flexible model based on the ZTP distribution for modeling lifetime data.