Abstract
In this study, we present a new family of continuous distributions via an extended form of the Weibull distribution. Some special members of the newly defined family are discussed and the new univariate continuous distributions are introduced. The mathematical properties are obtained for any members of the family such as expansions of the density, hazard rate function, quantile function, moments and order statistics. We obtain the distribution parameters by maximum likelihood method. The simulation study to evaluate the performance of the estimated parameters based on the selected member of the this new family is also given. The lifetime data example is discussed to illustrate the applicability of the distribution.
Highlights
The ordinary distributions can not always be su¢ cient to model the real data
We present a new family of continuous distributions via an extended form of the Weibull distribution
We studied its general structural properties such as expansions for density, quantile functions, moments, moment generating functions and order statistics under general settings
Summary
The ordinary distributions can not always be su¢ cient to model the real data. in many applied areas such as lifetime analysis there is a strong need for extended forms of the ordinary distributions. Its hazard rate function (hrf), de...ned by h (x; ) = g (x; )/(1 G (x; )), has the monotone shaped such as decreasing, increasing, and constant shaped These properties can be inadequate for the Weibull distribution since the empirical approaches to real data are often non-monotone hrf shapes such as unimodal, bathtube, and various shaped speci...cally in the lifetime applications. There are some generated families based on ordinary Weibull distribution in the literature. The aim of the paper is to propose a new ‡exible family of distributions based on T-X family using the EW as the generator In this way, we will utilize the ‡exibility of the baseline distribution for modelling the data.
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