Unit Interval Exponentiated Exponential Distribution and Quantile Regression Model: Applications for the COVID-19 Data and Bounded Responses Data

Abstract

The aim of this research is to propose the bounded exponentiated exponential (BEE) distribution for modeling the datasets on the unit interval e.g., between [0,1]. The proposed unit interval distribution is used to develop a quantile regression model. Continuous probability distributions are very useful to model lifetime data sets. Every single probability distribution is not suitable for all kinds of data sets. Therefore, proposing a new density can always be useful if showing the versatility and flexibility in it. Bounded exponentiated exponential distribution is developed by transforming the variable. The proposed density function exhibits different shapes which show its flexibility over different kinds of data sets. Many statistical and reliability properties of the BEE distribution have been developed. Few estimations methods have been discussed to estimate the parameters of the BEE distribution and a monte Carlo simulation study has been done. Subsequently, the applications of the BEE distribution are illustrated using COVID-19 data. Finally, several properties of the quantile regression model are derived, and the model is also applied on a unit interval response variable data set. For the purpose of modeling dependence between measures in a dataset, a bivariate extension of the proposed distribution is also developed. Furthermore, the bivariate model can be extended toward the development of its properties and applications.