The Gamma log-logistic Weibull distribution: model, properties and application

In this paper, a new generalized distribution called the gamma log-logistic Weibull (GLLoGW) distribution is proposed and studied. The GLLoGW distribution include the gamma log-logistic, gamma log-logistic Rayleigh, gamma log logistic exponential, log-logistic Weibull, log-logistic Rayleigh, log-logistic exponential, log-logistic as well as other special cases as sub-models. Some mathematical properties of the new distribution including moments, conditional moments, mean and median deviations, Bonferroni and Lorenz curves, distribution of the order statistics and R\'enyi entropy are derived. Maximum likelihood estimation technique is used to estimate the model parameters. A Monte Carlo simulation study to examine the bias and mean square error of the maximum likelihood estimators is presented and an application to real dataset to illustrate the usefulness of the model is given.