A Novel Family of Distribution with Application in Engineering Problems: A Simulation Study

Abstract

We establish a novel family of Kumaraswamy-X probability distributions in the present investigation. We discussed the Kumaraswamy Exponential univariate probability distribution. The new distribution with three parameters possesses density function with unimodal and reverse J-shape and hazard rate function of bathtub shaped. We study various statistical properties for it and derive the expressions for its density function, distribution function, survival and hazard rate function, Probability weighted Moments, lth moment, moment generating function, quantile function and Shannon entropy. For the derived distribution order statistics is also discussed. The parameters are estimated using the maximum likelihood estimation approach, and the performance of the estimators was evaluated using a Monte Carlo simulation. Through extensive Monte Carlo simulations and comparative analyses, we assess the
performance of the Kumaraswamy-X distribution against other common probability distributions used in engineering contexts. When we apply it to real datasets, it offers a more suitable fit than other existing distributions. We explore the characteristics and potential applications of the Kumaraswamy-X distribution in the context of engineering problems through a comprehensive simulation-based investigation