Transmuted cosine Topp-Leone G family of distributions: properties and applications

In contemporary data analysis, the need for flexible and adaptable probabilistic models capable of capturing complex dependencies and tail behaviors in real-life datasets has become increasingly apparent. In light of this demand, A new trigonometric generalized family of distribution, the "Transmuted Cosine Topp-Leone G Family" is proposed in this study. Established on the foundations of, this family combines the adaptability of the Topp-Leone distribution with the periodicity of the cosine function and transmutation theory to produce a flexible framework that may be used to represent a wide range of real-life phenomena. We derive some of the statistical properties of the introduced family such as; survival and hazard functions, and moment and moment-generating functions. Moreover, the model parameters are estimated using the Maximum Likelihood method, and a Monte Carlo simulation was performed to ascertain the behavior and the consistency of the estimates. We investigate the shape of the distribution parameters which results in distributions with left-skew, right-skew, increasing, and decreasing shapes. Lastly, through empirical demonstrations, we showcase the efficacy of the family TrCTLG models in fitting lifetime datasets.