The Kth-Order Equilibrium Rayleigh Distribution: Characterization and Estimation

Abstract

This paper introduces a new extension of Rayleigh distribution named as the Kth-order equilibrium Rayleigh distribution (KERD), by employing the concept of Kth order equilibrium method.  Various statistical properties of the new distribution, including its aging behavior and stochastic ordering relations, are analyzed. Explicit expressions are derived for moments, conditional moments, incomplete moments, the mean residualfunction, the mean waiting function, entropy measures, and order statistics. Distribution characterization has been examined. Maximum likelihood estimation method is used to estimate the parameters. A simulation study using the Anderson–Darling test statistic is carried out to analyze the asymptotic behavior of maximum likelihood estimators. The behaviors of bias and mean square error are observed with the increase in sample size. The applications of new distribution are demonstrated using two different real life datasets. Ultimately, a comparison is conducted among
KERD and its sub-models regarding their fit using Information Criterion tools.