Kumaraswamy Sine Inverted Rayleigh distribution : Properties and Application to Bladder Cancer Data

Abstract In this work, we propose the Kumaraswamy Sine Inverted Rayleigh distribution (KWSIR) as an improved version of the classical inverse Rayleigh distribution. The KWSIR distribution combines the Kumaraswamy and Sine Inverted Rayleigh distributions to provide better fits for real datasets. It is characterized by a unimodal and right-skewed probability density function, as well as an increasing and J-shaped hazard rate function. We explore various characteristics of this distribution, such as the probability density function, cumulative distribution function, quantile function, moments, incomplete moments entropy measures, and order statistics. The model parameters are estimated using maximum likelihood. Additionally, we demonstrate specific applications and provide examples to illustrate the flexibility and fitting capabilities of the model for real-world datasets 2010 Mathematics Subject Classification. 26A25; 26A35.