A new reciprocal Rayleigh extension: properties, copulas, different methods of estimation and a modified right-censored test for validation

Haitham M. Yousof; M. Masoom Ali; Hafida Goual; Mohamed Ibrahim

doi:10.21307/stattrans-2021-029

A new reciprocal Rayleigh extension: properties, copulas, different methods of estimation and a modified right-censored test for validation

Haitham M. Yousof Department of Statistics, Mathematics and Insurance, Faculty of Commerce, Benha University, Benha 13518, Egypt ORCID:https://orcid.org/0000-0003-4589-4944 , M. Masoom Ali Department of Mathematical Sciences Ball State University, Muncie, Indiana 47306, USA ORCID:https://orcid.org//0000-0002-0120-9442 , Hafida Goual Laboratory of Probability and Statistics, University of Badji Mokhtar, Annaba, Algeria ORCID:https://orcid.org/0000-0003-4932-4332 , Mohamed Ibrahim Department of Applied, Mathematical and Actuarial Statistics, Faculty of Commerce, Damietta University, Damietta, Egypt ORCID:https://orcid.org/0000-0003-4893-9669 Statistics in Transition new series, vol. 22, 2021, 3, pages: 99–121 Published online: 6 September 2021 DOI 10.21307/stattrans-2021-029

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ABSTRACT

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.

KEYWORDS

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

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