Abstract
A new generalized distribution called the {\em log-logistic modified Weibull} (LLoGMW) distribution is presented. This distribution includes many submodels such as the log-logistic modified Rayleigh, log-logistic modified exponential, log-logistic Weibull, log-logistic Rayleigh, log-logistic exponential, log-logistic, Weibull, Rayleigh and exponential distributions as special cases. Structural properties of the distribution including the hazard function, reverse hazard function, quantile function, probability weighted moments, moments, conditional moments, mean deviations, Bonferroni and Lorenz curves, distribution of order statistics, L-moments and R\'enyi entropy are derived. Model parameters are estimated based on the method of maximum likelihood. Finally, real data examples are presented to illustrate the usefulness and applicability of the model.
Highlights
Distribution theory because of its widespread applications in many fields such as finance, economics, physics, just to cite a few, has spawned the statistical literature
There is no significant difference between the log-logistic modified Weibull (LLoGMW) and the log-logistic Weibull (LLoGW) or log-logistic Rayleigh (LLoGR) distributions based on the likelihood ratio (LR) test
The values of the statistics: Akaike Information Criterion (AIC), AICC, and Bayesian Information Criterion (BIC) are smaller for the LLoGW distribution, the goodness-of-fit statistics W∗ and A∗ are the smallest and definitely points to the LLoGMW distribution as the “best”fit for the failure time data when compared to the values for the sub-models
Summary
Distribution theory because of its widespread applications in many fields such as finance, economics, physics, just to cite a few, has spawned the statistical literature. To lessen the complexity of these distribution, while Rajarshi and Rajarshi (1988) presented a revised version of these distributions, Haupt and Schabe (1992) on the other hand put forward a new lifetime model with bathtub-shaped failure rates. New classes of distributions based on modified versions of the Weibull distribution were presented to satisfy non-monotonic failure rate For such distributions, the reader can refer to Mudholkar and Srivastava (1993), and Pham and Lai (2007) for more details. The primary motivations for considering this new distribution are the advantages it offers with respect to having hazard functions that exhibits increasing, decreasing and bathtub shapes, as well as the versatility and flexibility in modeling lifetime data.
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