New Distribution with Statistical Properties and Classical Estimation Method

Abstract

In the present study, we propose a new model, identified as the Shanker Rayleigh distribution, which is derived by combining the survival functions of the classical Rayleigh and Shanker distributions, both of which have a scale parameter only. We developed this hybrid model to offer the additional modeling flexibility required for complex lifespans that single-unit distributions cannot accurately represent. Theoretical characteristics of the distribution (probability density function, cumulative distribution function, survival, and hazard rate function) are derived in closed form. In addition, important distributional properties, namely the raw and central moments, moment-generating function, and quantile function, are methodically examined and developed from two statistical methods, maximum likelihood estimation (MLE) and ordinary least squares (OLS), for estimating the parameter of the proposed model, and their efficiency was assessed by applying them to real data to demonstrate the new models’ ability to better apply the data. In addition, this proposal was applied for scientific purposes through the analysis of real data