Power Size Biased Two-Parameter Akash Distribution

Alhyasat Khaldoon (), Kamarulzaman Ibrahim, Al-Omari Amer Ibrahim () and Abu Bakar Mohd Aftar ()
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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 .

Statistics in Transition New Series, 2020, vol. 21, issue 3, 73-91

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.

Keywords: 62E10; 62F15; Akash distribution; two-parameter Akash distribution; size-biased distribution; moments; coefficient of variation; coefficient of skewness; coefficient of kurtosis; maximum likelihood estimation; entropy. (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:stintr:v:21:y:2020:i:3:p:73-91:n:4

DOI: 10.21307/stattrans-2020-045

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