The Half Logistic Log-logistic Weibull Distribution: Model, Properties and Applications

Abstract

new three parameter distribution named Half Logistic Log-Logistic Weibull (HLLLW) distribution is developed. This model includes Half Logistic Log-Logistic (HLLL) distribution, Half Logistic Log-Logistic Exponential (HLLLE) distribution and Half Logistic Log-Logistic Rayleigh (HLLLR) distribution as sub-models. Structural properties including shapes, hazard function, reverse hazard function, quantile function, moments, conditional moments, mean deviations, Bonferroni and Lorenz Curves, R´enyi entropy and distribution of order statistics are presented. We adopt the maximum likelihood method to estimate model parameters. To check the accuracy of the maximum likelihood estimates, various simulations were performed for different parameter settings and sample sizes. Finally, numerical examples are provided to test the goodness of fit of the proposed model compared to other models.