The Exponential-Reciprocal Generalized Inverse Gaussian distribution. A new model to describe loss distributions

Abstract

A new family of probability distributions with support in (0, ∞) is introduced here. This new family is obtained through the mixture of the exponential distribution with the reciprocal of the generalized inverse Gaussian distribution. We show some important features such as expressions of probability density function, moments, etc. Special attention is paid to the mixture with the reciprocal of the inverse Gaussian distribution, as a particular case of the reciprocal of the generalized inverse Gaussian distribution. This distribution can be considered competitive to the exponential-inverse Gaussian distribution in Frangos and Karlis (2004) and has a more simple formulation than this. The ver..