Shako Kumaraswamy distributions with properties and applications in different fields

Abstract

The Shako Kumaraswamy distribution is a novel and adaptable extension of the Kumaraswamy distribution that is presented in this paper. By adding a shape parameter, the suggested model expands on the traditional Kumaraswamy distribution and improves its ability to present a variety of distributional shapes and tail behaviours. The probability density function, quantile function, cumulative distribution function, moments, and other reliability metrics are all derived as part of a thorough mathematical analysis. Additionally, limiting behaviours and special situations are analysed to demonstrate the generality of the suggested distribution. The behaviour of the estimators under various sample sizes and parameter settings is evaluated in a thorough Monte Carlo simulation study to evaluate the effectiveness of the parameter estimation techniques. Additionally, the Shako Kumaraswamy distribution's practicality is illustrated using two real-world data sets from different domains.