Abstract
：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.
Highlights
Burr XII distribution is a well known parametric model that has found wide application in different fields such as reliability, income and biological sciences
We propose a model that is flexible in accommodating various hazard functions which are likely to be encountered in practical situations
Adeniyi F.Fagbamigbe distribution plays an important role in income, we construct and develop the statistical properties of this new class of generalized distribution called the exponentiated Burr XII Weibull distribution and apply it to real lifetime data in order to demonstrate the usefulness of the proposed distribution
Summary
Burr XII distribution is a well known parametric model that has found wide application in different fields such as reliability, income and biological sciences. Haupt and Schabe [10] developed a new lifetime model with bathtub-shaped failure rates It has been shown in the literature that exponentiated distributions are flexible enough to accommodate in many cases both monotone as well as bath-tub hazard rates. The primary motivation for the development of the exponentiated Burr XII Weibull distribution is the modeling of lifetime data and other data types with a diverse model that takes into consideration shape and scale, and skewness, kurtosis and tail variation. Adeniyi F.Fagbamigbe distribution plays an important role in income, we construct and develop the statistical properties of this new class of generalized distribution called the exponentiated Burr XII Weibull distribution and apply it to real lifetime data in order to demonstrate the usefulness of the proposed distribution.
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