Abstract
A new generalized class of distributions called the Burr-Weibull Power Series (BWPS) class of distributions is developed and explored. This class of distributions generalizes the Burr power series and Weibull power series classes of distributions, respectively. A special model of the BWPS class of distributions, the new Burr-Weibull Poisson (BWP) distribution is considered and some of its mathematical properties are obtained. The BWP distribution contains several new and well known sub-models, including Burr-Weibull, Burr-exponential Poisson, Burr-exponential, Burr-Rayleigh Poisson, Burr-Rayleigh, Burr-Poisson, Burr, Lomax-exponential Poisson, Lomax-Weibull, Lomax-exponential, Lomax-Rayleigh, Lomax-Poisson, Lomax, Weibull, Rayleigh and exponential distributions. Maximum likelihood estimation technique is used to estimate the model parameters followed by a Monte Carlo simulation study. Finally an application of the BWP model to a real data set is presented to illustrate the usefulness of the proposed class of distributions.
Highlights
The Burr XII (Burr) distribution is a very useful model that was first discussed by Burr (1942) as a two-parameter family
The primary motivation for developing the class of Burr-Weibull Power Series (BWPS) distributions is the versatility and flexibility derived from compounding continuous distributions including the new distribution called Burr-Weibull distribution with power series distributions to obtain a new class of distributions with desirable properties including hazard function that exhibits increasing, decreasing, bathtub and upside down bathtub shapes
Another important reason for the development of the BWPS class of distributions is the modeling of income and lifetime data with a model that takes into consideration shape and scale and skewness, kurtosis and tail variation
Summary
The Burr XII (Burr) distribution is a very useful model that was first discussed by Burr (1942) as a two-parameter family. Including the new distribution called Burr-Weibull distribution with power series distributions to obtain a new class of distributions with desirable properties including hazard function that exhibits increasing, decreasing, bathtub and upside down bathtub shapes Another important reason for the development of the BWPS class of distributions is the modeling of income and lifetime data with a model that takes into consideration shape and scale and skewness, kurtosis and tail variation. Motivated by various applications of power series distributions in several areas including reliability, exponential tilting (weighting) in finance and actuarial sciences, as well as economics we construct and develop the statistical properties of this new class of generalized compound distribution called the Burr-Weibull Power Series class of distributions and apply it to real lifetime data in order to demonstrate the usefulness of the proposed distribution.
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