Abstract
This paper considers and studies a distinct special case of omega distribution defined on the unit interval (0, 1), called unit-omega distribution. Thanks to its simple form, some of its basic properties are derived. The maximum likelihood method, Bayes method, and the method of moments are used to estimate the parameters of unit-omega distribution. These estimation methods are examined by conducting a simulation study. More importantly, the quantile function of unit-omega distribution has a closed-form expression that allows modeling the conditional quantiles of a unit response variable as a function of covariates. Residual analysis is performed using randomized quantile residuals and Cox–Snell residuals. The proposed approach is used to model the quantiles of child mortality rates, conditional on covariates. These covariates represent the proportions of people left behind across three key indicators: nutrition, availability of safe drinking sources and adequate education. Another application that relates to recovery rates of viable CD34+ cell is presented. From both applications, the fitting results of the proposed regression model outperform those of beta, Kumaraswamy and unit-Weibull regression models.