Novas medidas de bondade de ajuste para a família Kumaraswamy-G: uma aplicação a dados hidrológicos

Abstract

In this essay, we propose GoF measures for generalized Kumaraswamy (Kw-G) models based on the Mellin Transform (MT) and Probability Weighted Moments (PWM). We combine PWMs and the MT in order to furnish new GoF quantitative tools for choosing models within the Kw-G class. First, we derive PWMs for the Exp-Weibull, Exp-Fréchet, Exp-loglogistic and Exp-Uniform distributions. After, we provide expressions for the MT associated with the Kw-G family and some of its special cases: in particular, Kumaraswamy-Weibull, Kumaraswamy-Fréchet, Kumaraswamy-log-logistic and Kumaraswamy distributions. Subsequently, we make a combination between the Hotelling’s T2 statistic and the multivariate Delta method to test hypotheses involving second kind cumulants. Finally, we apply the proposed GoF measures on four real data sets applications in hydrology contexts.