Estimation and diagnostic tools in reparameterized slashed Rayleigh regression model: an application to chemical data

Abstract

In this paper, we introduce a regression model where the response variable is reparameterized slashed Rayleigh (RSR) distributed and which is indexed by mean and precision parameters. The proposed regression model is useful for situations where the variable of interest is continuous and restricted to the positive real line and is related to other variables through the mean and precision parameters. In addition, the RSR model has properties that its competitor distributions of the exponential family do not have. Estimation is performed by expectation maximization (EM) and extensions. Furthermore, we discuss residuals and influence diagnostic tools. Finally, we also carry out two applications to real-world data that demonstrate the usefulness of the proposed model.