Parameter Estimation for the Exponentiated Kumaraswamy-Power Function Distribution Based on Order Statistics with Application

  • Devendra KumarEmail author
  • Neetu Jain
  • Mazen Nassar
  • Osama Eraki Abo-Kasem


Exponentiated Kumaraswamy-power function (EKPF) distribution has been proposed recently by Bursa and Ozel (Hacet J Math Stat 46:277–292, 2017) as a quite flexible in terms of probability density and hazard rate functions than power function distribution. In this paper, we obtain the explicit expressions for the single, double (product), triple and quadruple moments and moment generating function for single, double, triple and quadruple of order statistics of the EKPF distribution. By using these relations, we have tabulated the means and variances of order statistics from samples of sizes up to 10 for various values of the parameters. We use five frequentist estimation methods to estimate the unknown parameters and a simulation study is used to compare the performance of the different estimators. Finally, we analyse a real data set for illustrative purpose.


Exponentiated Kumaraswamy-power function Order statistics Moments and moment generating function Estimations Monte Carlo simulation 



The authors would like to thank the reviewer and the editor for their comments that helped improve the article substantially.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of StatisticsCentral University of HaryanaAdalpurIndia
  2. 2.Department of StatisticsUniversity of DelhiNew DelhiIndia
  3. 3.Department of Statistics, Faculty of ScienceKing Abdulaziz UniversityJeddahKingdom of Saudi Arabia
  4. 4.Department of Statistics, Faculty of CommerceZagazig UniversityZagazigEgypt

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