The Exponentiated Burr XII Weibull Distribution: Model, Properties and Applications

Boikanyo Makubate ； Neo Dingalo ； Broderick O. Oluyede ； Adeniyi F.Fagbamigbe

《Journal of Data Science》 16卷3期 (2018/07) Pp. 431-463

https://doi.org/10.6339/JDS.201807_16(3).0001

摘要

A new distribution called the exponentiated Burr XII Weibull(EBW) distributions is proposed and presented. This distribution contains several new and known distributions such as exponentiated log-logistic Weibull, exponentiated log-logistic Rayleigh, exponentiated log-logistic exponential, exponentiated Lomax Weibull, exponentiated Lomax Rayleigh, exponentiated Lomax Exponential, Lomax Weibull, Lomax Rayleigh Lomax exponential, Weibull, Rayleigh, exponential and log-logistic distributions as special cases. A comprehensive investigation of the properties of this generalized distribution including series expansion of probability density function and cumulative distribution function, hazard and reverse hazard functions, quantile function, moments, conditional moments, mean deviations, Bonferroni and Lorenz curves, R'enyi entropy and distribution of order statistics are presented. Parameters of the model are estimated using maximum likelihood estimation technique and real data sets are used to illustrate the usefulness and applicability of the new generalized distribution compared with other distributions.

關鍵字

Burr XII distribution ； Exponentiated Distribution ； Maximum Likelihood Estimation ； Weibull Distribution