A dynamic stochastic version of the pitcher‐hamblin‐miller model of “collective violence"*

I am indebted to Walter Kristof and the reviewers of the Journal of Mathematical Sociology for critical and helpful comments.

The central equation of the deterministic diffusion model of Pitcher, Hamblin, and Miller (1978) is formulated as a time‐inhomogeneous stochastic process. It will be shown that the stochastic process leads to a negative binomial distribution. The deterministic diffusion function can be derived from the stochastic model and is identical to the expected value as a function of time. Therefore the deterministic model is supported in terms of the underlying stochastic process. Moreover the stochastic model allows the prediction of the distribution for any point in time and the construction of prediction intervals.

Notes

I am indebted to Walter Kristof and the reviewers of the Journal of Mathematical Sociology for critical and helpful comments.