The Log-logistic Weibull Distribution with Applications to Lifetime Data

Abstract

In this paper, a new generalized distribution called the log-logistic Weibull (LLoGW) distribution is developed and presented. This dis- tribution contain the log-logistic Rayleigh (LLoGR), log-logistic expo- nential (LLoGE) and log-logistic (LLoG) distributions as special cases. The structural properties of the distribution including the hazard func- tion, reverse hazard function, quantile function, probability weighted moments, moments, conditional moments, mean deviations, Bonferroni and Lorenz curves, distribution of order statistics, L-moments and Renyi entropy are derived. Method of maximum likelihood is used to estimate the parameters of this new distribution. A simulation study to examine the bias, mean square error of the maximum likelihood estimators and width of the condence intervals for each parameter is presented. Finally, real data examples are presented to illustrate the usefulness and applicability of the model.