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

• Authors: Haitham M. Yousof , M. Masoom Ali , Hafida Goual , Mohamed Ibrahim

Abstracts

EN

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

EN

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

• Publisher: Główny Urząd Statystyczny
• Journal: Statistics in Transition new series
• Year: 2021
• Volume: 22
• Issue: 3
• Pages: 99-121

Contributors

author

Haitham M. Yousof

• Department of Statistics, Mathematics and Insurance, Faculty of Commerce, Benha University, Benha, Egypt
• Department of Mathematical Sciences Ball State University, Muncie, Indiana, USA

• https://orcid.org/0000000345894944

author

M. Masoom Ali

• Department of Mathematical Sciences Ball State University, Muncie, Indiana, USA

• https://orcid.org/0000000201209442

author

Hafida Goual

• Laboratory of Probability and Statistics, University of Badji Mokhtar, Annaba, Algeria

• https://orcid.org/0000000349324332

author

Mohamed Ibrahim

• Department of Applied, Mathematical and Actuarial Statistics, Faculty of Commerce, Damietta University, Damietta, Egypt

• https://orcid.org/0000000348939669

Identifiers

DOI

10.21307/stattrans-2021-029

Biblioteka Nauki

1827545