Abstract
We propose and develop the properties of a new generalized distribution called the beta log-logistic Weibull (BLLoGW) distribution. This model contain several new distributions such as beta log-logistic Rayleigh, beta log-logistic exponential, exponentiated log-logistic Weibull, exponentiated log-logistic Rayleigh, exponentiated log-logistic exponential,  log-logistic Weibull, log-logistic Rayleigh and log-logistic distributions as special cases. Structural properties of this generalized distribution including series expansion of the probability density function and cumulative distribution function, hazard function, reverse hazard function, quantile function, moments, conditional moments, mean deviations, Bonferroni and Lorenz curves, R\'enyi entropy and distribution of order statistics are presented. The parameters of the distribution are estimated using maximum likelihood estimation technique. A Monte Carlo simulation study is conducted to examine the bias and mean square error of the maximum likelihood estimates. A real dataset is used to illustrate the applicability and usefulness of the new generalized distribution.
Highlights
Generalized distributions are of tremendous practical importance and have recieved considerable attention by many authors in recent years. Eugene, Lee and Famoye (2002) introduced a generalized beta distributions and presented results on the beta normal distribution
We propose and develop the properties of a new generalized distribution called the beta log-logistic Weibull (BLLoGW) distribution
Motivated by various applications of log-logistic, Weibull and beta distributions in several areas including reliability, exponential tilting in finance and actuarial sciences, as well as economics, where loglogistic distribution plays an important role in income, we construct and develop the statistical properties of this new class of generalized distribution called the beta log-logistic Weibull distribution and apply it to real lifetime data in order to demonstrate the usefulness of the proposed distribution
Summary
Generalized distributions are of tremendous practical importance and have recieved considerable attention by many authors in recent years. Eugene, Lee and Famoye (2002) introduced a generalized beta distributions and presented results on the beta normal distribution. Eugene, Lee and Famoye (2002) introduced a generalized beta distributions and presented results on the beta normal distribution. Nadarajah, Cordeiro & Ortega (2012) presented general results on the beta modified Weibull distribution. Motivated by various applications of log-logistic, Weibull and beta distributions in several areas including reliability, exponential tilting (weighting) in finance and actuarial sciences, as well as economics, where loglogistic distribution plays an important role in income, we construct and develop the statistical properties of this new class of generalized distribution called the beta log-logistic Weibull distribution and apply it to real lifetime data in order to demonstrate the usefulness of the proposed distribution.
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