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Power Size Biased Two-Parameter Akash Distribution

Author

Listed:
  • Alhyasat Khaldoon

    (School of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia, 43600 UKM Bangi, Malaysia .)

  • Kamarulzaman Ibrahim

    (School of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia, 43600 UKM Bangi, Malaysia .)

  • Al-Omari Amer Ibrahim

    (School of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia, 43600 UKM Bangi, Malaysia .)

  • Abu Bakar Mohd Aftar

    (Department of Mathematics, Faculty of Science, Al al-Bayt University, Mafraq, Jordan .)

Abstract

In this paper, the two-parameter Akash distribution is generalized to size-biased two-parameter Akash distribution (SBTPAD). A further modification to SBTPAD is introduced, creating the power size-biased two-parameter Akash distribution (PSBTPAD). Several statistical properties of PSBTPAD distribution are proved. These properties include the following: moments, coefficient of variation, coefficient of skewness, coefficient of kurtosis, the maximum likelihood estimation of the distribution parameters, and finally order statistics. Moreover, plots of the density and distribution functions of PSBTPAD are presented and a reliability analysis is considered. The Rényi entropy of PSBTPAD is proved and the application of real data is discussed.

Suggested Citation

  • Alhyasat Khaldoon & Kamarulzaman Ibrahim & Al-Omari Amer Ibrahim & Abu Bakar Mohd Aftar, 2020. "Power Size Biased Two-Parameter Akash Distribution," Statistics in Transition New Series, Statistics Poland, vol. 21(3), pages 73-91, September.
    • Handle: RePEc:vrs:stintr:v:21:y:2020:i:3:p:73-91:n:4
    DOI: 10.21307/stattrans-2020-045
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    References listed on IDEAS

    as
    1. Ghitany, M.E. & Al-Mutairi, D.K. & Balakrishnan, N. & Al-Enezi, L.J., 2013. "Power Lindley distribution and associated inference," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 20-33.
    2. Kamlesh Kumar Shukla & Rama Shanker, 2018. "Power Ishita Distribution And Its Application To Model Lifetime Data," Statistics in Transition New Series, Polish Statistical Association, vol. 19(1), pages 135-148, March.
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