A New Class of Generalized Log-Logistic Weibull Distribution: Theory, Properties and Applications

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Journal of Probability and Statistical Sciences


A new generalized distribution called the exponentiated log-logistic Weibull (ELLoGW) distribution is developed and presented. This class of distributions contains exponentiated log-logistic Rayleigh, exponentiated log-logistic exponential, log-logistic Weibull, log-logistic Rayleigh, log-logistic exponential, log-logistic, Weibull, Rayleigh, exponential and several other distributions as special cases. The structural properties of the distribution including hazard function, reverse hazard function, quantile function, moments, conditional moments, mean deviations, Bonferroni and Lorenz curves, entropy and order statistics are derived. The method of maximum likelihood is used to estimate the model parameters and finally, real data examples are discussed to illustrate the applicability of the distribution.