The Alpha Power Transformation Family: Properties and Applications

Mohamed E. Mead, Gauss M. Cordeiro, Ahmed Z. Afify, Hazem Al Mofleh

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.


Keywords


Alpha Power Family, Exponentiated Weibull Distribution, Maximum Likelihood, Moment,Order Statistic.

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DOI: http://dx.doi.org/10.18187/pjsor.v15i3.2969

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Title

The Alpha Power Transformation Family: Properties and Applications

Keywords

Alpha Power Family, Exponentiated Weibull Distribution, Maximum Likelihood, Moment,Order Statistic.

Description

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.


Date

2019-09-07

Identifier


Source

Pakistan Journal of Statistics and Operation Research; Vol. 15 No. 3, 2019



Print ISSN: 1816-2711 | Electronic ISSN: 2220-5810