Abstract
In this paper, a new generalized distribution called the log-logisticWeibull (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 weightedmoments, moments, conditional moments, mean deviations, Bonferroniand Lorenz curves, distribution of order statistics, L-moments and Renyientropy are derived. Method of maximum likelihood is used to estimatethe parameters of this new distribution. A simulation study to examinethe bias, mean square error of the maximum likelihood estimators andwidth of the condence intervals for each parameter is presented. Finally, real data examples are presented to illustrate the usefulness and applicability of the model.
Highlights
There are several generalizations of univariate distributions including those of (Eugene, Lee, and Famoye 2002) dealing with the beta-normal distribution, as well general family of univariate distributions generated from the Weibull distribution that was introduced by Gurvich, Dibenedetto, and Ranade (1997)
We propose and study this new distribution called the log-logistic Weibull distribution which inherits these desirable properties and covers quite a variety of shapes
We present the distribution of the ith order statistic from the log-logistic Weibull (LLoGW) distribution
Summary
There are several generalizations of univariate distributions including those of (Eugene, Lee, and Famoye 2002) dealing with the beta-normal distribution, as well general family of univariate distributions generated from the Weibull distribution that was introduced by Gurvich, Dibenedetto, and Ranade (1997). Later on, (Rajarshi and Rajarshi 1988) presented a revision of these distributions, and (Haupt and Schabe 1992) put forward a new lifetime model with bathtub-shaped failure rates. To motivate the model under study, consider a series system and assume that the lifetime of the components follow the log-logistic and Weibull distributions with with reliability functions. A primary motivation for developing this model is the advantages presented by this generalized distribution with respect to having a hazard function that exhibits increasing, decreasing and bathtub shapes, as well as the versatility and flexibility of the log-logistic and Weibull distributions in modeling lifetime data. Applications of the proposed model to real data are given in section 8, followed by concluding remarks
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