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

Abstract

In this work, we introduce the Kumaraswamy Sine Inverted Rayleigh (KWSIR) distribution as an extension of the classical Inverse Rayleigh distribution, offering greater flexibility in modeling real-world data. The KWSIR distribution combines the Kumaraswamy and Sine Inverted Rayleigh distributions, resulting in a unimodal, right-skewed probability density function and an increasing or J-shaped hazard rate function. We explore key statistical properties, including the probability density function, cumulative distribution function, quantile function, moments, incomplete moments, entropy measures, and order statistics. Parameter estimation is conducted using the maximum likelihood method. To illustrate its applicability, we analyze a real-world dataset on bladder cancer, demonstrating the superior fitting performance of the KWSIR distribution.

Keywords: Probability distribution; maximum likelihood estimation; moments, moment generating function.

2010 Mathematics Subject Classification. 26A25; 26A35