A NEW CLASS OF COS-G FAMILY OF DISTRIBUTIONS WITH APPLICATIONS

This paper introduces a novel family of probability distributions, termed the Cos-G family, which is derived from a trigonometric transformation approach. We present the general structural properties of this family and focus on one of its unique members. This newly proposed distribution, formulated from the inverse Weibull distribution, exhibits flexible hazard rate shapes, including reverse-J, increasing, and inverted bathtub forms. We investigate its fundamental statistical properties and employ the maximum likelihood estimation method to estimate its parameters. The performance of the estimation technique is assessed through a Monte Carlo simulation, revealing that biases and mean square errors decrease as sample size increases, ensuring reliable parameter estimation even for small samples. To illustrate its practical applicability, we fit the suggested model to three real-world datasets and compare its performance against existing models using various goodness-of-fit measures and model selection criteria. The results confirm the superiority of the proposed model in capturing complex data structures.