Development and Exploration of Cosine Rayleigh Distribution

This study introduces a novel trigonometric extension of the Rayleigh distribution, the Cosine Rayleigh (CR) distribution. This new distribution is formulated by compounding the Rayleigh distribution with the Cosine G family of distributions. We derive the statistical properties of the CR distribution, including moments, hazard function, survival function, entropy measure, and order statistics. To estimate the parameter of the CR distribution, we employed sixteen different techniques, such as maximum likelihood, Anderson-Darling, Cramer-von Mises, maximum product of spacings, least squares, percentile, right-tail Anderson-Darling, weighted least squares, left-tail Anderson-Darling, minimum spacing absolute distance, minimum spacing absolute-log distance, Anderson-Darling left-tail second order, Kolmogorov, minimum spacing square distance, minimum spacing square-log distance, and minimum spacing Linex distance. A simulation study was conducted to evaluate the performance of the sixteen estimation methods. The results showed that all sixteen estimators produced consistent parameter estimates, with the maximum likelihood method emerging as the best in terms of accuracy. The practical utility of the CR distribution was demonstrated by fitting it to two real-life data sets and comparing its goodness-of-fit with other competing models, including the baseline Rayleigh distribution. The results indicated that the CR model provides a superior fit, highlighting its potential applicability in various fields involving lifetime data.