Modelo de regressão Kumaraswamy modal aplicado à distorção idade-série nas cidades da região Norte do Brasil

Abstract

The Kumaraswamy probability distribution, proposed by Kumaraswamy (1980), is a continuous model with support in the interval (0,1), similar to the beta model. Like the beta distribution, the Kumaraswamy distribution is suitable for analyzing data representing rates or proportions. However, the mean of the Kumaraswamy distribution does not have a simple expression, making it challenging to create a regression structure based on the mean. Despite this fact, some studies have worked with the Kumaraswamy distribution in the context of regression, such as the work developed by Mitnik e Baek (2013), which proposes a model based on reparameterization for the median. In this work, a reparameterization for the Kumaraswamy distribution in terms of the mode, called the modal Kumaraswamy distribution, is studied, along with the regression model based on this reparameterized distribution. The aim is to provide an alternative model for data of this nature and, furthermore, one that is useful for the analysis of asymmetric data. A simulation study is also conducted to assess the performance of the maximum likelihood estimator and the coverage probabilities of asymptotic confidence intervals. This suggests good performance, especially for data with a sample size equal to or greater than 100. An application of the modal Kumaraswamy regression model to the age-grade distortion in students aged 6 to 14 years attending elementary school in cities in the northern region of Brazil in 2010 is presented. Finally, the modal Kumaraswamy model is compared with the modal Beta and Unit-Gompertz regression models.