A comparative study of estimation methods for the New Sine Topp-Leone Fréchet distribution

Modeling and fitting complex datasets are crucial domains in various scientific fields. This article presents the sine Topp-Leone Fréchet distribution, a new probability distribution obtained by integrating the Fréchet distribution with the sine Topp-Leone-G family. The suggested model’s most noteworthy feature is its ability to accurately represent a broad variety of hazard rate patterns (such as upside-down, reversed J-shaped, decreasing, and increasing) with just three parameters. Its density may also display unimodal, reversed-J, and right-skewed shapes. We offer a number of statistical properties for the proposed distribution. Using sixteen different estimation approaches, we estimated the parameters of the suggested model and investigated a number of its distributional characteristics. We evaluate the validity of the suggested model and compare the efficacy of various parameter estimates using a Monte Carlo simulation. Numerical analysis shows that the Kolmogorov and second-order left-tail Anderson–Darling estimators exhibit superior efficiency and consistency in a variety of scenarios. They frequently receive the highest overall ranking based on the sum of all performance criteria and consistently produce estimates with low bias and mean squared error. Additionally, we evaluated the suggested distribution’s adaptability using two real-world datasets, demonstrating its remarkable ability to precisely fit the data. According to our findings, the suggested distribution performs better in terms of fit quality than a cotangent Fréchet, odd exponential-logarithmic Fréchet, Topp-Leone Fréchet, odd-generalized exponential inverse Weibull, generalized inverse Weibull distribution, arctan inverse Weibull, new arctan Fréchet, and Fréchet distributions.