The Weibull Exponential {Logistic} Poisson Distribution: Properties and Application

Abstract

This paper introduces the Weibull Exponential {Logistic} Poisson Distribution (WELPD), a new five-parameter lifetime distribution obtained by compounding the Weibull Exponential {Logistic} distribution of (Eno et al., 2022) with the power series family of distributions proposed by (Osatohanmwen et al., 2020). The probability density function, cumulative distribution function, survival function, and hazard function are derived. Comprehensive statistical properties including the quantile function, moments, moment generating function, skewness, and kurtosis are investigated. The parameters are estimated using the method of maximum likelihood. The flexibility and superiority of the proposed distribution are demonstrated through application to real life data of the failure times of electric bulbs dataset. The results indicate that the WELPD provides a better fit compared to the Weibull Exponential {Logistic} Distribution (WELD) and the Weibull Logistic Distribution (WLD), as evidenced by lower values of the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Kolmogorov-Smirnov (K-S) statistic, Cramér-von Mises (CM) statistic, and Anderson-Darling (AD) statistic.