Exponential distribution, Cosine function, Mathematical properties, Estimation, Simulation, Reliability sector, Engineering (General). Civil engineering (General), TA1-2040

This article delves into the critical role that probability-focused methodologies play in the fields of reliability sciences and the arts, ultimately leading to the introduction of a novel statistical model known as the new cosine exponentiated exponential (NCE-exponential) distribution. This model is a synthesis of the well-established exponentiated exponential distribution and a cosine-based probabilistic framework, which together offer a more versatile tool for statistical analysis. The research presented in this article meticulously explores the mathematical properties of the NCE-exponential distribution, with a particular emphasis on its quartile features. In addition to theoretical exploration, the article discusses point estimators for the unknown parameters of the NCE-exponential model. A simulation study, which serves to validate the effectiveness of the model estimators, is also provided. Furthermore, the article highlights practical applications of the NCE-exponential distribution in both reliability sciences and the arts. By leveraging four fundamental evaluation tools, it is clear that the NCE-exponential distribution achieves a superior fit when contrasted with adversarial distributions. The findings of this research suggest that the NCE-exponential distribution not only enhances the toolkit available for statisticians and researchers but also expands the range of probability distributions that can be employed for real-world statistical analysis.