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In this paper, we propose a closed form approximation to the mean andvariance of a new generalization of negative binomial (NGNB) distributionarising from the Extended COM-Poisson (ECOMP) distribution developed byChakraborty and Imoto (2016)(see [4]). The NGNB is a special case of the ECOMPdistribution and was named so by these authors. This distribution is moreflexible in terms of the dispersion index as compared to its ordinarycounterparts. It approaches the COM-Poisson distribution (Shmueli et al. 2005)[11] under suitable limiting conditions. The NGNB can also be obtained from theCOM-Negative Hypergeometric distribution (Roy et al. 2019)[10] as a limitingdistribution. In this paper, we present closed-form approximations for the meanand variance of the NGNB distribution. These approximations can be viewed asthe mean and variance of convolution of independent and identically distributednegative binomial populations. The proposed closed-form approximations of themean and variance will be helpful in building the link function for thegeneralized negative binomial regression model based on the NGNB distributionand other extended applications, hence resulting in enhanced applicability ofthis model.

A Closed Form Approximation of Moments of New Generalization of Negative Binomial Distribution