A note on a variance bound for the multinomial and the negative multinomial distribution

TL;DR

This paper establishes a Chernoff-type upper variance bound for the multinomial and negative multinomial distributions, providing a theoretical tool for understanding their variability.

Contribution

It introduces a new variance bound for these distributions, extending existing theoretical results and including an application example.

Findings

Proved a Chernoff-type variance bound for multinomial distribution.

Extended the variance bound to negative multinomial distribution.

Provided an application demonstrating the bound's usefulness.

Abstract

We prove a Chernoff-type upper variance bound for the multinomial and the negative multinomial distribution. An application is also given.