Stochastic modeling of a serial killer
Abstract
We analyze the time pattern of the activity of a serial killer, who during twelve years had murdered 53 people. The plot of the cumulative number of murders as a function of time is of "Devil's staircase" type. The distribution of the intervals between murders (step length) follows a power law with the exponent of 1.4. We propose a model according to which the serial killer commits murders when neuronal excitation in his brain exceeds certain threshold. We model this neural activity as a branching process, which in turn is approximated by a random walk. As the distribution of the random walk return times is a power law with the exponent 1.5, the distribution of the inter-murder intervals is thus explained. We illustrate analytical results by numerical simulation. Time pattern activity data from two other serial killers further substantiate our analysis.
Cite
@article{arxiv.1201.2458,
title = {Stochastic modeling of a serial killer},
author = {M. V. Simkin and V. P. Roychowdhury},
journal= {arXiv preprint arXiv:1201.2458},
year = {2014}
}