# A New Mixed Generalized Negative Binomial Distribution

## TL;DR

This paper introduces a new five-parameter generalized negative binomial distribution, derives its properties, and demonstrates its application on automobile insurance data, expanding statistical modeling options.

## Contribution

It presents a novel five-parameter generalized distribution with derived properties and demonstrates its practical application to insurance data.

## Key findings

- Distribution has flexible modeling capabilities.
- Maximum likelihood estimates are derived.
- Applied successfully to automobile insurance data.

## Abstract

In this article, a generalized version of Negative binomial-beta exponential distribution with five parameters have been introduced. Some interesting submodels have been derived from it. A comprehensive mathematical treatment of proposed distribution is being provided. Various expressions like that of moment generating function, moments are derived. The model parameters are estimated by the maximum likelihood method. Finally, the application of proposed distribution is carried out on one sample of automobile insurance data.