Polish Statistical Association

Central Statistical Office of Poland

**Subject:** Economics, Statistics & Probability

**ISSN:** 1234-7655

**eISSN:** 2450-0291

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Haitham M. Yousof
** ^{*}**
/
M. Masoom Ali

**Keywords : **
Xgamma model,
reciprocal Rayleigh model,
simulations,
bootstrapping,
Farlie Gumbel Morgenstern copula,
least squares,
Cramer-Von-Mises,
bootstrapping,
Ali-Mikhail-Haq copula,
convexity,
concavit

**Citation Information : **
Statistics in Transition New Series. Volume 22,
Issue 3,
Pages 99-121,
DOI: https://doi.org/10.21307/stattrans-2021-029

**License : **
(CC BY-NC-ND 4.0)

**Received Date : **24-January-2020
/
**Accepted: **01-June-2021
/
**Published Online: ** 05-September-2021

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In this article, a new reciprocal Rayleigh extension called the Xgamma reciprocal Rayleigh model is defined and studied. The relevant statistical properties are derived, and the useful results related to the convexity and concavity are addressed. We discussed the estimation of the parameters using different estimation methods such as the maximum likelihood estimation method, the ordinary least squares estimation method, the weighted least squares estimation method, the Cramer-Von-Mises estimation method, and the bootstrapping method. A simulation study was conducted to assess the performances of the proposed estimation methods are investigated through a simulation study. Many bivariate and multivariate type model have also been derived based on Farlie-Gumbel-Morgenstern copula, the Clayton copula, Renyi’s entropy copula and the Ali-Mikhail-Haq copula. A modified Nikulin-Rao-Robson test for right-censored validation is applied to a censored real data set.

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