In this paper, we propose a new distribution for modeling count datasets with some unique characteristics, obtained by mixing the generalized Poisson distribution (GPD) and the generalized inverse Gaussian distribution (GIGD) and using the framework of the Lagrangian probability distribution. Some structural properties of the proposed new distribution are discussed. Parameter estimates are computed using the method of maximum likelihood. A real-life data set is used to examine the performance of the new distribution.

generalized Poisson distribution, generalized inverse Gaussian distribution, Bessel approximation, Lagrangian probability distribution, maximum likelihood.