Revision as of 09:50, 17 November 2025

Abstract

Many lifetime analysis, such as engineering, biology, survival, actuarial and medical sciences, heavily rely on the two-parameter compound Rayleigh exponential distribution, which is well-known in statistical theory. Because of their ability to successfully handle small sample sizes and involve prior knowledge, Bayesian techniques are crucial for estimating the parameters of the compound Rayleigh exponential distribution. This study presents the estimation of the compound Rayleigh exponential distribution unknown parameters using Bayesian and non-Bayesian estimation techniques, including maximum likelihood estimation, maximum product spacing, least square estimator, weighted least square estimator, Cramer-Von-Mise estimator, Anderson-Darling estimator, and Bayesian techniques with informative and non-informative priors based on different loss functions. Additionally, we used several methods to obtain the confidence intervals for the unknown parameters, such as the approximate and Bootstrap methods. The effectiveness of these estimators is evaluated through a Monte Carlo simulation study. Furthermore, we are committed to investigating three widely recognized risk metrics: the value at risk, the tail value at risk, and the tail variance premium. These findings are helpful for actuarial risk researchers who depend on risk measurement fitting when evaluating Bayesian tools for effectively modeling actuarial sciences. Finally, different applications taken from several areas are examined to illustrate the practical usefulness of the compound Rayleigh exponential distribution. Using various model selection criteria, the introduced model is contrasted with that of several well-known distributions. Our empirical findings indicate that the suggested model has superior goodness-of-fit to the other models examined.

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