Deriving the new cotangent Fréchet distribution with real data analysis

Abstract

This study introduces the family of the novel ”cot-generator” distributions based on the cotangent function. The construction of the probability density function based on the cot-generator and its corresponding moments, reliability indicators, and order statistics are derived. Regarding inferential procedures, the maximum likelihood estimation method is implemented to estimate the model parameters in a non-closed form. The novel Cot-Fréchet distribution (NCFD) is then focused on a specific class member, constructed using the Fréchet distribution as the baseline. The estimators’ bias, variance, and mean square error (MSE) efficiency are examined and evaluated through Monte Carlo simulation experiments. The novel model is also applied to some real data sets to assess its efficacy and is compared with other competing distributions.