Using the Censored Gamma Distribution for Modelling Fractional Response Variables with an Application to Loss Given Default

Regression models for limited continuous dependent variables having a non-negligible probability of attaining exactly their limits are presented. The models differ in the number of parameters and in their flexibility. Fractional data being a special case of limited dependent data, the models also apply to variables that are a fraction or a proportion. It is shown how to fit these models and they are applied to a Loss Given Default dataset from insurance to which they provide a good fit.

Keywords: Fractional response variables; censored distributions; Tobit models; limited dependent variables; Loss Given Default