Development, Theoretical Properties and Simulation Assessment of the Exponential Weibull Log-Logistic Poisson Distribution and Its Regression Model

Abstract

In an effort to address for the family of distribution that permits flexibility in simulating real-world phenomena, a new family of univariate probability distribution called exponential Weibull log-logistic Poisson family of probability distribution is introduced in this paper by compounding the T- R [Y] family of distribution. The new distribution has the advantage of being capable of modeling various shapes of ageing and failure criteria. We derive several of its structural properties including moment, survival function, hazard function and order statistics. The new density function can be expressed as a linear mixture of exponentiated Weibull densities. We proposed a linear regression model using a new distribution–the exponential Weibull log-logistic Poisson distribution. The maximum-likelihood method is used to estimate the model parameters and simulation results were provided to assess the performance of the proposed maximum-likelihood procedure. The results of this study offer a strong basis for real-world applications.