Negative Binomial-Reciprocal Inverse Gaussian Distribution: Statistical Properties with Applications in Count Data

Abstract

In this paper, a new count distribution has been introduced by mixing negative binomial with reciprocal inverse Guassian distribution. This model is tractable with some important properties not only limited to actuarial science but in other fields as well where over-dispersion pattern is seen. A recurrence relation for the probabilities of the new distribution and an integral equation for the probability density function of the compound version, when the claim severities are absolutely continuous, are derived. Brief idea about its respective multivariate version are also given. Parameters involved in the proposed model have been estimated by maximum likelihood estimation technique. Finally, applications of the model to real data sets are presented and compared with the fit attained by some
other well-known one and two-parameter distributions.