The Unit Omega Distribution, Properties and Its Application

Abstract

Dombi et al. introduced the omega distribution with three positive parameters and proved that its asymptotic distribution is the Weibull model. We propose the unit omega distribution with support in ( 0 , 1 ) , and obtain a linear representation for its density function. The maximum likelihood and Bayesian methods are adopted for estimating the model parameters. It is conducted Monte Carlo simulations to examine the means, biases, and square roots of the mean square errors of the maximum likelihood estimators. The importance of the new distribution is proved by means of antimicrobial resistance data.