A Discrete Analogue of Complementary Exponentiated-G Poisson Family of Distributions: Properties and Estimation
A. G. AL-Kashlan
Department of Statistics, Faculty of Commerce, AL-Azhar University (Girls’ Branch), Tafahna Al-Ashraf, Egypt.
M. A. Hegazy
Department of Statistics, Faculty of Commerce, AL-Azhar University (Girls’ Branch), Tafahna Al-Ashraf, Egypt.
A. A. EL-Helbawy *
Department of Statistics, Faculty of Commerce, AL-Azhar University (Girls’ Branch), Cairo, Egypt.
*Author to whom correspondence should be addressed.
Abstract
This paper presented a two discrete family of life distributions called discrete complementary exponentiated-G Poisson family and discrete Zubair-G family as a special case from discrete complementary exponentiated-G Poisson family. Some basic distributional properties are derived. Such as hazard rate, moments, quantiles, order statistics and Rényi Entropy. A special sub-model of the discrete Zubair-G family, called the discrete Zubair Weibull distribution is considered in detail. Discrete Zubair exponential distribution and discrete Zubair Rayleigh distribution are obtained as two special cases from discrete Zubair Weibull distribution. Method of maximum likelihood is used under Type-II censored samples for estimating the unknown parameters, survival, hazard rate and alternative hazard rate functions. Confidence intervals for the parameters are obtained. A simulation study is carried out to illustrate the theoretical results of the maximum likelihood estimation. Finally, the performance of the new distribution is compared with existing distributions using applications of three real data sets to show the suitability and flexibility of the proposed model.
Keywords: Complementary exponentiated-G Poisson, Discrete order statistic, Markov Chain Monte Carlo method, Maximum likelihood method, Moments, Quantile function, Type-II censored samples, Weibull distribution, Zubair-G distribution