Distributional Nikulin-Rao-Robson validity under a novel gamma extension with characterizations and risk assessment

Document Type : Special Issue Dedicated to memory of Prof. Mahbanoo Tata

Authors

1 Department of Mathematical and Statistical Sciences, Marquette University, USA

2 Department of Quantitative Methods, School of Business, King Faisal University, Al-Ahsa 31982, Saudi Arabia

3 Department of Applied Statistics and Insurance, Faculty of Commerce, Mansoura University, Mansoura 35516, Mansoura, Egypt

4 Laboratory of probability and statistics LaPS, University Badji Mokhtar, Annaba, Algeria

5 Department of Statistics, American University, Cairo, Egypt

6 Department of Statistics, Cornell University, Ithaca, NY, USA

7 Department of Statistics, Mathematics and Insurance, Benha University, Benha, Egypt

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

Abstract

In this work, a novel probability distribution is introduced and studied. Some characterizations are presented. Several financial risk indicators, such as the value-at-risk, tail-valueat-risk, tail variance, tail Mean-Variance, and mean excess loss function are considered under the maximum likelihood estimation, the ordinary least squares, the weighted least squares, and the Anderson Darling estimation methods. These four methods were applied for the actuarial evaluation under a simulation study and under an application to insurance claims data. For distributional validation under the complete data, the well-known Nikulin-Rao-Robson statistic is considered. The Nikulin-Rao-Robson test statistic is assessed under a simulation study and under three complete real data sets. For censored distributional validation, a new version of the Nikulin-Rao-Robson statistic is considered. The new Nikulin-Rao-Robson test statistic is assessed under a comprehensive simulation study and under three censored real data sets.

Keywords

Main Subjects

References

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Journal of Mahani Mathematical Research
Volume 13, Issue 3 - Serial Number 28
Special Issue Dedicated to Memory of Professor Mahbanoo Tata
August 2024
Pages 1-32

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  • Receive Date: 15 February 2024
  • Accept Date: 16 March 2024

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