A new probability Chen model: Properties, risk analysis and distributions validation for testing using the right censored real data

Ibrahim, Mohamed; H. Al-Nefaie, Abdullah; M. AboAlkhair, Ahmad; Ali, M. Masoom; Aidi, Khaoula; Yousof, Haitham M.

doi:10.21608/cjmss.2025.395958.1208

A new probability Chen model: Properties, risk analysis and distributions validation for testing using the right censored real data

Document Type : Original Article

Authors

¹ Department of Quantitative Methods, School of Business, King Faisal University, Al Ahsa 31982, Saudi Arabia

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

³ Department of Mathematical Sciences, Ball State University, Muncie, IN, USA

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

⁵ Department of Statistics, Mathematics and Insurance, Benha University, Benha, Egypt

10.21608/cjmss.2025.395958.1208

Abstract

This paper introduces and explores a new flexible probability distribution called the BXGZC model, with a focus on its properties, applications in actuarial risk analysis, and validation using real-world right-censored data. The proposed model builds upon the Chen distribution, offering enhanced adaptability for modeling both positively and negatively skewed da-tasets commonly encountered in insurance and financial risk assessment. We examine several key risk indicators, such as Value-at-Risk (VaR), Tail-Value-at-Risk (TVaR), tail variance, tail mean-variance, and the mean excess loss function, and apply them under different estimation techniques including maximum likelihood, ordinary least squares, weighted least squares, and Cramer–von Mises methods. These approaches are tested through simulation studies involving various sample sizes to evaluate their performance in capturing risk measures accurately. Additionally, we apply the BXGZC model to re-al-life insurance claims data to assess its practical utility in actuarial evaluation. To further validate the model’s fit, espe-cially in the context of censored data, we employ a modified version of the Nikulin–Rao–Robson goodness-of-fit test. This test is particularly useful when dealing with survival or reliability data where censoring is present. The results demonstrate that the BXGZC model outperforms the standard Chen distribution in fitting a wide range of right-censored datasets across different domains such as medical research, engineering reliability, and insurance. It provides actuaries and risk analysts with a more robust and versatile tool for modeling extreme losses, quantifying tail behavior, and making informed decisions under uncertainty.

Keywords