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Stochastic catastrophe models and multimodal distributions
Author(s) -
Cobb Loren
Publication year - 1978
Publication title -
behavioral science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 45
eISSN - 1099-1743
pISSN - 0005-7940
DOI - 10.1002/bs.3830230407
Subject(s) - probabilistic logic , catastrophe theory , stochastic modelling , nonlinear system , statistical physics , statistical model , stochastic process , mathematical economics , econometrics , computer science , mathematics , statistics , physics , engineering , geotechnical engineering , quantum mechanics
Nonlinear models such as have been appearing in the applied catastrophe theory literature are almost universally deterministic, as opposed to stochastic (probabilistic). The purpose of this article is to show how to convert a deterministic catastrophe model into a stochastic model with the aid of several reasonable assumptions, and how to calculate explicitly the resulting multimodal equilibrium probability density. Examples of such models from epidemiology, psychology, sociology, and demography are presented. Lastly, a new statistical technique is presented, with which the parameters of empirical multimodal frequency distributions may be estimated.