A stochastic evolutionary model generating a mixture of exponential distributions

TL;DR

This paper extends a stochastic urn-based model to generate mixtures of exponential distributions, effectively capturing heterogeneity in human dynamics data, validated through empirical analysis of search engine query survival times.

Contribution

The paper introduces a novel extension of an existing stochastic model to produce mixture exponential distributions, enhancing modeling of human behavioral heterogeneity.

Findings

Model accurately fits search query survival data

Mixture model captures data heterogeneity effectively

Empirical validation over 114 months of data

Abstract

Recent interest in human dynamics has stimulated the investigation of the stochastic processes that explain human behaviour in various contexts, such as mobile phone networks and social media. In this paper, we extend the stochastic urn-based model proposed in \cite{FENN15} so that it can generate mixture models,in particular, a mixture of exponential distributions. The model is designed to capture the dynamics of survival analysis, traditionally employed in clinical trials, reliability analysis in engineering, and more recently in the analysis of large data sets recording human dynamics. The mixture modelling approach, which is relatively simple and well understood, is very effective in capturing heterogeneity in data. We provide empirical evidence for the validity of the model, using a data set of popular search engine queries collected over a period of 114 months. We show that the survival function of these queries is closely matched by the exponential mixture solution for our model.