Advances and Applications in Statistics
Volume 51, Issue 2, Pages 85 - 129
(August 2017) http://dx.doi.org/10.17654/AS051020085 |
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LOG-EXPONENTIATED KUMARASWAMY POWER SERIES FAMILY OF DISTRIBUTIONS
S. K. Ashour, D. R. Said and M. A. Mostafa
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Abstract: In this paper, we introduce a new distribution which is obtained by compounding the log-exponentiated Kumaraswamy and power series distributions. This new distribution is called the log-exponentiated Kumaraswamy-power series (Log-EKPS) distributions. This family contains several new distributions such as log-exponentiated Kumaraswamy geometric distribution, log-exponentiated Kumaraswamy Poisson distribution, log-exponentiated Kumaraswamy logarithmic distribution and log-exponentiated Kumaraswamy binomial distribution. We discuss some properties of the Log-EKPS such as its moments and generating function, the density function of the order statistics, quantiles, median, mode, Lorenz and Bonferroni curves, mean deviations. The method of maximum likelihood is used for estimating the model parameters via EM algorithm. Special distributions are investigated in some detail. An application to a real data set is analyzed to illustrate the flexibility of the new distributions. |
Keywords and phrases: log-exponentiated Kumaraswamy distribution, order statistic, power series distribution, maximum likelihood estimation. |
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