The Generalized Half-Cauchy Distribution: Mathematical Properties and Regression Models with Censored Data

摘要

We study some mathematical properties of a new generalized half-Cauchy distribution, which extends the classical half-Cauchy model. We derive a power series expansion for the quantile function, explicit expressions for the ordinary and incomplete moments and generating function, order statistics and their moments. We also present characterizations of the generalized half-Cauchy distribution. The estimation of the model parameters is performed by maximum likelihood. We introduce thelog -generalized half-Cauchy regression model based on the half-Cauchy distribution. The new regression model represents a parametric family of models that includes as special cases several widely known regression models that can be applied to censored survival data. In addition, the sensitivity analysis is proposed and the empirical distribution of some modified residuals are displayed and compared with the standard normal distribution. We demonstrate the potentiality of the new models by means of two applications to two real data.