Simulation of negative binomial processes

Abstract

Three simple stochastic models that can be used to generate correlated negative binomial variates are proposed. Two of the models are constructed according to the autoregressive scheme of the first—order Markovian process. The third model is constructed via the Poisson process from a first—order autoregressive gamma sequence and the resulting process has the long—term correlation structure of the mixed autoregressive moving—average process.

Keywords:

• Autoregressive
• moving—average processes
• negative binomial distribution
• gamma distribution
• simulation