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

Author

Listed:
  • Yousof Haitham M.

    (Department of Statistics, Mathematics and Insurance, Faculty of Commerce, Benha University, Benha, 13518, Egypt .)

  • Masoom Ali M.

    (Department of Mathematical Sciences Ball State University, Muncie, Indiana, 47306, United States .)

  • Goual Hafida

    (Laboratory of Probability and Statistics, University of Badji Mokhtar, Annaba, Algeria .)

  • Ibrahim Mohamed

    (Department of Applied, Mathematical and Actuarial Statistics, Faculty of Commerce, Damietta University, Damietta, Egypt .)

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.

Suggested Citation

  • Yousof Haitham M. & Masoom Ali M. & Goual Hafida & Ibrahim Mohamed, 2021. "A new reciprocal Rayleigh extension: properties, copulas, different methods of estimation and a modified right-censored test for validation," Statistics in Transition New Series, Polish Statistical Association, vol. 22(3), pages 99-121, September.
    • Handle: RePEc:vrs:stintr:v:22:y:2021:i:3:p:99-121:n:7
    DOI: 10.21307/stattrans-2021-029
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    References listed on IDEAS

    as
    1. Mahmoud M. Mansour & Mohamed Ibrahim & Khaoula Aidi & Nadeem Shafique Butt & Mir Masoom Ali & Haitham M. Yousof & Mohamed S. Hamed, 2020. "A New Log-Logistic Lifetime Model with Mathematical Properties, Copula, Modified Goodness-of-Fit Test for Validation and Real Data Modeling," Mathematics, MDPI, vol. 8(9), pages 1-20, September.
    2. Mukhtar M. Salah & M. El-Morshedy & M. S. Eliwa & Haitham M. Yousof, 2020. "Expanded Fréchet Model: Mathematical Properties, Copula, Different Estimation Methods, Applications and Validation Testing," Mathematics, MDPI, vol. 8(11), pages 1-29, November.
    3. Faton Merovci & Morad Alizadeh & Haitham M. Yousof & G. G. Hamedani, 2017. "The exponentiated transmuted-G family of distributions: Theory and applications," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(21), pages 10800-10822, November.
    4. Haitham M. Yousof & Ahmed Z. Afify & Saralees Nadarajah & Gokarna R. Aryal, 2018. "The Marshall-Olkin Generalized-G Family Of Distributions With Applications," Statistica, Department of Statistics, University of Bologna, vol. 78(3), pages 273-295.
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    Cited by:

    1. Haitham M. Yousof & Hafida Goual & Walid Emam & Yusra Tashkandy & Morad Alizadeh & M. Masoom Ali & Mohamed Ibrahim, 2023. "An Alternative Model for Describing the Reliability Data: Applications, Assessment, and Goodness-of-Fit Validation Testing," Mathematics, MDPI, vol. 11(6), pages 1-26, March.
    2. Heba Soltan Mohamed & M. Masoom Ali & Haitham M. Yousof, 2023. "The Lindley Gompertz Model for Estimating the Survival Rates: Properties and Applications in Insurance," Annals of Data Science, Springer, vol. 10(5), pages 1199-1216, October.
    3. Mohamed Ibrahim & Khaoula Aidi & M. Masoom Ali & Haitham M. Yousof, 2023. "A Novel Test Statistic for Right Censored Validity under a new Chen extension with Applications in Reliability and Medicine," Annals of Data Science, Springer, vol. 10(5), pages 1285-1299, October.

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