THE UNIT POWER RAYLEIGH DISTRIBUTION AND APPLICATIONS

Abstract

The Rayleigh distribution is commonly used to model the lifespan of objects or service times. This paper introduces a new distribution called the ”Unit Power Rayleigh Distribution” with support on the unit interval (0, 1). We explore its statistical properties such as density function, survival function, hazard function, moments, Quantile function, and order statistic. We estimate the unknown parameters using the maximum likelihood method. Simulation schemes are designed to illustrate its behavior. Finally, we apply the model to a real-world dataset and demonstrate its superiority over its special cases by comparing the goodness of fit.