Modified Kumaraswamy distributions for double bounded hydro-environmental data

Abstract

In this paper, we propose two-parameter probability models referred to as modified Kumaraswamy (MK) and reflected modified Kumaraswamy (RMK) distributions for modeling hydro-environmental data in the unit interval. The MK distribution presents increasing-decreasing-increasing density shapes while the RMK distribution presents decreasing-increasing-decreasing shapes, which are not obtained in classical distributions for modeling double bounded data, such as the beta and Kumaraswamy. Some statistical properties are derived, such as moments and quantile function. We also consider the maximum likelihood approach for parameter estimation and perform a Monte Carlo simulation study to evaluate the performance of the estimators on synthetic hydro-environmental data. Finally, an empirical application to the percentage of useful volume of 37 Brazilian water reservoirs is presented and discussed. The modeled densities and goodness-of-fit measures evidence that the proposed distributions outperform the beta and Kumaraswamy models, being suitable alternatives for modeling hydro-environmental data.