Generalized Odd Power Cauchy Family and Its Associated Heteroscedastic Regression Model

Abstract

This study introduces a generalization of the odd power Cauchy family by adding one more shape parameter togain more flexibility modeling the complex data structures. The linear representations for the density, moments, quantile,and generating functions are derived. The model parameters are estimated employing the maximum likelihood estimationmethod. The Monte Carlo simulations are performed under different parameter settings and sample sizes for the proposedmodels. In addition, we introduce a new heteroscedastic regression model based on the special member of the proposedfamily. Three data sets are analyzed with competitive and proposed models.