Statistical Properties and Estimation of Power-Transmuted Inverse Rayleigh Distribution


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Statistics in Transition New Series

Polish Statistical Association

Central Statistical Office of Poland

Subject: Economics, Statistics & Probability


ISSN: 1234-7655
eISSN: 2450-0291





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VOLUME 21 , ISSUE 3 (September 2020) > List of articles

Statistical Properties and Estimation of Power-Transmuted Inverse Rayleigh Distribution

Amal S. Hassan / Salwa M. Assar / Ahmed M. Abdelghaffar

Keywords : transmuted inverse Rayleigh, mean residual life function, maximum likelihood, percentiles

Citation Information : Statistics in Transition New Series. Volume 21, Issue 3, Pages 93-107, DOI:

License : (CC BY-NC-ND 4.0)

Received Date : 21-November-2019 / Accepted: 14-June-2020 / Published Online: 20-September-2020



A three-parameter continuous distribution is constructed, using a power transformation related to the transmuted inverse Rayleigh (TIR) distribution. A comprehensive account of the statistical properties is provided, including the following: the quantile function, moments, incomplete moments, mean residual life function and Rényi entropy. Three classical procedures for estimating population parameters are analysed. A simulation study is provided to compare the performance of different estimates. Finally, a real data application is used to illustrate the usefulness of the recommended distribution in modelling real data.

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