Statistical properties and different methods of estimation for extended weighted inverted 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 2 (June 2020) > List of articles

Statistical properties and different methods of estimation for extended weighted inverted Rayleigh distribution

Abhimanyu Singh Yadav * / S. K. Singh / Umesh Singh

Keywords : moments and inverse moments, entropy measurements, order statistics, classical methods of estimation

Citation Information : Statistics in Transition New Series. Volume 21, Issue 2, Pages 119-141, DOI:

License : (CC BY-NC-ND 4.0)

Received Date : 03-May-2017 / Accepted: 13-February-2020 / Published Online: 01-June-2020



The aim of this paper is to introduce a new weighted probability distribution to model the non-monotone failure rate pattern for survival data. The proposed distribution is generalized by considering inverted Rayleigh distribution as a baseline distribution called an extended weighted inverted Rayleigh distribution. Different statistical properties such as moment, quantile function, moment generating function, entropy measurement, Bonferroni and Lorenz curve, stochastic ordering and order statistics have been derived. Different estimation procedures have also been discussed to estimate the unknown parameters of the proposed probability distribution. The Monte Carlo simulation study has been conducted to compare the performances of the proposed estimators obtained through various methods of estimation. Finally, two real data sets have been used to show the applicability of the proposed model in a real-life scenario.

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