Kumaraswamy regression modeling for Bounded Outcome Scores

Abstract

In this paper, we use a regression model for modeling bounded outcome scores (BOS), where the outcome is Kumaraswamy distributed. Similar to the Beta distribution, this distribution can take a variety of shapes while being computationally easier to use. Thus, it is deemed as a suitable alternative distribution to the Beta in modeling bounded random processes. In the proposed model, the median of a bounded response is modeled by the linear predictors which is defined through regression parameters and explanatory variables. We obtained the maximum likelihood estimates (MLE) of the parameters, provided closed-form expressions for the score functions and Fisher information matrix, and presented some diagnostic measures. We conducted Monte Carlo simulations to investigate the finite-sample performance of the MLEs of the parameters. Finally, two practical applications of this model to the real data sets are presented and discussed.

New Goodness-of-Fit Tests for the Kumaraswamy Distribution

“…In contrast, the median of the Kumaraswamy distribution has a simple form, given in Equation (5), and so robust regression based on this distribution is straightforward. See Mitnik and Baek [16] and Hamedi-Shahraki et al [17], for example.…”