The Sine Topp-Leone Exponentiated Inverted Kumaraswamy Distribution and its Application on Environmental Data

Abstract

This paper introduces a new four-parameter lifetime continuous distribution, derived by compounding the Topp-Leone exponentiated inverted Kumaraswamy model with the Sine-G family of distributions. The resulting model is named the Sine Topp-Leone Exponentiated Inverse Kumaraswamy distribution. It exhibits considerable flexibility, with its probability density function (pdf) capable of being positively or negatively skewed, symmetric, unimodal, increasing, or decreasing. The study explores key statistical and mathematical properties of the new model, including the quantile function, median, moments, moment generating function, hazard function, and survival function. Additionally, the pdfs of the minimum and maximum order statistics were derived and analyzed. Model parameters were estimated using the maximum likelihood estimation method, and a simulation study was conducted to evaluate the consistency of the estimator. Finally, real-life datasets were applied to demonstrate the model’s effectiveness and adaptability, comparing it with other competing models like the Topp-Leone exponentiated inverse Kumaraswamy, inverse Kumaraswamy, and Kumaraswamy distributions.