Abstract
In this paper, we introduce a new four-parameter distribution called the transmuted Weibull power function (TWPF) distribution which e5xtends the transmuted family proposed by Shaw and Buckley [1]. The hazard rate function of the TWPF distribution can be constant, increasing, decreasing, unimodal, upside down bathtub shaped or bathtub shape. Some mathematical properties are derived including quantile functions, expansion of density function, moments, moment generating function, residual life function, reversed residual life function, mean deviation, inequality measures. The estimation of the model parameters is carried out using the maximum likelihood method. The importance and flexibility of the proposed model are proved empirically using real data sets.
Highlights
There are hundreds of continuous distributions in the statistical literature
This section is devoted to main properties of the transmuted Weibull power function (TWPF) distribution, quantile function, moments and moment generating function. 3.1
This subsection concerns with the μr′ moment and moment generating function for the TWPF distribution
Summary
There are hundreds of continuous distributions in the statistical literature These distributions have several applications in many applied fields such as reliability, life testing, biomedical sciences, economics, finance, environmental and engineering, among others. 398 Transmuted Weibull Power Function Distribution: its Properties and Applications xβ F(x; α, β) = (α) , βxβ−1 f(x) = αβ , 0 < x < α, β > 0 where β is a shape parameter and α is a scale parameter. The need for extended forms of the PF distribution arises in many applied areas and some generalizations of the PF distribution have been proposed. Aryal and Tsokos [10] presented a new generalization of Weibull distribution called the transmuted Weibull distribution. The aim of this paper is to define and study a new flexible lifetime model called the transmuted Weibull power function (TWPF) distribution.
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