  In this article, we propose a new three parameter distribution by compounding
negative binomial with reciprocal inverse Gaussian model called negative
binomial-reciprocal inverse Gaussian distribution. This model is tractable with
some important properties not only in actuarial science but in other fields as
well where overdispersion pattern is seen. Some basic properties including
recurrence relation of probabilities for computation of successive
probabilities have been discussed. In its compound version, when the claims are
absolutely continuous, an integral equation for the probability density
function is discussed. Brief discussion about extension of univariate version
have also been done to its respective multivariate version. parameters involved
in the model have been estimated by Maximum Likelihood Estimation technique.
Applications of the proposed distribution are carried out by taking two real
count data sets. The result shown that the negative binomial-reciprocal inverse
Gaussian distribution gives better fit when compared to the Poisson and
negative binomial distributions.
