# On a flexible construction of a negative binomial model

## TL;DR

This paper introduces a flexible method for constructing stationary Markov models with negative-binomial marginals, providing explicit transition probabilities linked to birth and death processes, and demonstrates its effectiveness on simulated and real data.

## Contribution

It offers a novel closed-form construction of negative-binomial Markov models, connecting them to birth-death processes and enabling practical applications.

## Key findings

- Closed-form transition probabilities derived for the models
- Effective modeling demonstrated on simulated data
- Real data applications validate the approach

## Abstract

This work presents a construction of stationary Markov models with negative-binomial marginal distributions. A simple closed form expression for the corresponding transition probabilities is given, linking the proposal to well-known classes of birth and death processes and thus revealing interesting characterizations. The advantage of having such closed form expressions is tested on simulated and real data.