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We propose a new model with flexible failure rate called complementary Poisson generalized half logistic (CPGHL). Various properties of the model are explored and examine numerically such as the explicit expressions of the moments, mean deviations, Bonferroni and Lorenz curves, Shannon and Renyi entropy. The distribution of mixture of two CPGHL and some related models based on the log-transform of CPGHL are discussed. The asymptotic of moments of residual life and asymptotic distribution of order statistics are obtained. The characterization of Poisson half logistic (PHL) by truncated moments of a certain function of a random variable is discussed. Estimation of the model parameters was approached by maximum likelihood, least square, and percentile methods. Further, the estimation by maximum likelihood for right censored data of the model were considered. The proposed estimation techniques were assessed by simulation studies. Three data applications are provided one of them is a censored data to demonstrate how the new model outperforms some other existing distribution in practice.

A New Three Parameter Lifetime Model: The Complementary Poisson Generalized Half Logistic Distribution