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Abstract
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First we introduce and study some general mathematical properties of a new generator of continuous distributions with two extra shape parameters called the odd generalized half Cauchy family. A second goal, we introduce the new log-generalized odd half-Cauchy heteroscedastic regression model with censored data, which represents a parametric family of models that includes as sub-models several widely known regression models
that can be applied to data with no homogeneity of variance. Maximum likelihood estimation of the model parameters with censored data as well as a simulation study are investigated. We also prove empirically the flexibility of the new family by means real data sets.
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