On the Weibull-X family of distributions

Abstract

In this paper, the Weibull-X family is proposed and some of its properties are discussed. A member of the Weibull-X family, the Weibull-logistic distribution, is defined and studied. Various properties of the Weibull-logistic distribution are obtained. The distribution is found to be unimodal and the shape can be symmetric, right skewed or left skewed. The structural analysis of the distribution in this paper includes limiting behavior, mode, quantiles, moments, skewness, kurtosis, Shannon's entropy and order statistics. The method of maximum likelihood estimation is proposed for estimating the model parameters. A real data set is used to illustrate the application of the Weibull-logistic distribution.