Author(s):
1. Mohamed E. Mead:
Department of Statistics, Mathematics and Insurance, Faculty of Commerce, Zagazig University, Egypt
2. Gauss M. Cordeiro:
Departamento de Estat stica Universidade Federal de Pernambuco Recife, Pernambuco, Brazi
3. Ahmed Z. Afify:
Department of Statistics, Mathematics and Insurance, Benha University, Egypt
4. Hazem Al-Mofleh:
Department of Mathematics, Tafila Technical University, Tafila, Jordan
Abstract:
Mahdavi and Kundu (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 de ne 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, modi ed Weibull, transmuted Weibull and exponentiated Weibull distributions by means of two real data sets.
Page(s):
525-545
DOI:
DOI not available
Published:
Journal: Pakistan Journal of Statistics and Operation Research, Volume: 15, Issue: 3, Year: 2019
Keywords:
Maximum Likelihood
,
Order Statistic
,
Moment
,
Alpha Power Family
,
Exponentiated Weibull Distribution
References:
References are not available for this document.
Citations
Citations are not available for this document.