A New Family of Distributions: The Additive Modified Weibull Odd Log-logistic-G Poisson Family, Properties and Applications

Abstract

In this paper, a new family of distributions, called the additive modified Weibull odd log-logistic-G Poisson distribution, is proposed and studied. Some mathematical properties are presented and special models are discussed. We derive a power series for the quantile function, explicit expressions for the moments, quantile and generating functions and order statistics. we also consider some estimators of the PDF and the survival function of the new family such as: maximum likelihood estimator, percentile estimator, least squares estimator and weighted least squares estimator. Simulation studies and real data application are also considered for performance of the new family and comparing these estimators.