Abstract
Bathtub failure rate shape is widely used in industrial and medical applications. In this paper, a three-parameter lifetime distribution, so-called the generalized Weibull uniform distribution that extends the Weibull distribution, is proposed and studied. This distribution has bathtub-shaped or decreasing failure rate function which enables it to fit real lifetime data sets. Various structural properties of the new distribution are derived, including explicit expressions for the quantile function, moments, moment-generating function and order statistics. Parameter estimations are provided by a maximum likelihood estimation, and the performance of the maximum likelihood estimation is evaluated using a simulation study. An application to real-life data demonstrates that the proposed distribution can be very useful in fitting real data.
Highlights
In recent years, many classical distributions have been generalized by adding more shape parameters since numerous application in the field of engineering, financial, biomedical and environmental sciences indicated that classical distributions are not suitable to explain the data sets
Voltage data were employed to illustrate the flexibility of the generalized Weibull uniform (GWU) distribution, in addition to compare the behavior of the new model with other generalization of Weibull distribution
One set of real-life data was employed to demonstrate the flexibility of GWU distribution
Summary
Many classical distributions have been generalized by adding more shape parameters since numerous application in the field of engineering, financial, biomedical and environmental sciences indicated that classical distributions are not suitable to explain the data sets. Several trials have been conducted to define new generalizations of the Weibull distribution by adding several additional shape parameter(s), for instance, see [7, 13, 15, 19]. Cordeiro et al [6] proposed a generalized Weibull-G “GW-G” family of distributions by substituting the argument t with − loge{1 − G(t; )} in Eq (1) and defined the cdf of their family of distributions by. A generalization of the WU distribution, referred as a generalized Weibull uniform (GWU) distribution, is obtained The aim of this generalization is to provide a flexible extension of WU distribution which helps practitioners to model data for different fields. 2, statistical properties of the GWU distribution are obtained including the shapes of the pdf and FRF, quantile function (qf), moments and the moment-generating function.
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