Abstract
Mahdavi A. and Kundu D. (2017) introduced a family for generating univariate distributions called the alpha power transformation. They studied as a special case the properties of the alpha power transformed exponential distribution. We provide some mathematical properties of this distribution and define a four-parameter lifetime model called the alpha power exponentiated Weibull distribution. It generalizes some well-known lifetime models such as the exponentiated exponential, exponentiated Rayleigh, exponentiated Weibull and Weibull distributions. The importance of the new distribution comes from its ability to model monotone and non-monotone failure rate functions, which are quite common in reliability studies. We derive some basic properties of the proposed distribution including quantile and generating functions, moments and order statistics. The maximum likelihood method is used to estimate the model parameters. Simulation results investigate the performance of the estimates. We illustrate the importance of the proposed distribution over the McDonald Weibull, beta Weibull, modified Weibull, transmuted Weibull and exponentiated Weibull distributions by means of two real data sets.
Highlights
Mahdavi and Kundu (2017) proposed a new class of distributions called the alpha power transformation (APT) family
We present some simulation results to investigate the behavior of the maximum likelihood estimates (MLEs) in terms of the sample size n
We investigate some mathematical properties of the alpha power transformation family (Mahdavi and Kundu, 2017) and propose a new four-parameter model, named the alpha power exponentiated Weibull (APEW) distribution, which extends the well-known exponentiated Weibull distribution pioneered by Mudholkar et al (1995)
Summary
Mahdavi and Kundu (2017) proposed a new class of distributions called the alpha power transformation (APT) family. For an arbitrary parent cumulative distribution function (cdf) G(x), Mahdavi and Kundu (2017) defined the cdf of the APT family (for x ∈ R) by FAP T (x) =. A simple interpretation of the APT family, for a non-negative random variable X, is as follows. If Y represents the random variable of the investigator’s records, Y has the pdf (2). We study a new lifetime model, based on the APT family, called the alpha power exponentiated Weibull (APEW) distribution, and derive some of its structural properties.
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