Power Size Biased Two-Parameter Akash Distribution

Khaldoon  Alhyasat; Ibrahim  Kamarulzaman; Amer Ibrahim  Al-Omari; Mohd Aftar Abu Bakar

doi:DOI 10.21307/stattrans-2020-045

Power Size Biased Two-Parameter Akash Distribution

Khaldoon Alhyasat School of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia, 43600 UKM Bangi, Malaysia , Ibrahim Kamarulzaman School of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia, 43600 UKM Bangi, Malaysia , Amer Ibrahim Al-Omari School of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia, 43600 UKM Bangi, Malaysia ORCID:https://orcid.org/0000-0002-6901-8263 , Mohd Aftar Abu Bakar Department of Mathematics, Faculty of Science, Al al-Bayt University, Mafraq, Jordan ORCID:https://orcid.org/0000-0002-3009-6168 Statistics in Transition new series, vol. 21, 2020, 3, pages: 73-91 Published online: 4 September 2020 DOI DOI 10.21307/stattrans-2020-045

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ABSTRACT

In this paper, the two-parameter Akash distribution is generalized to size-biased twoparameter 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.

KEYWORDS

Akash distribution, two-parameter Akash distribution, size-biased distribution, moments, coefficient of variation, coefficient of skewness, coefficient of kurtosis, maximum likelihood estimation, entropy

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