Application of Catastrophe Theory for Multimodal Distributions Statistical Analysis

Abstract

This work considers the application of catastrophe theory methods (classification of smooth mappings) to the construction of analytical models of objects and processes based on statistical data. Multimodal one-dimensional statistical distributions are compared to catastrophe models of corank 1, i.e., the $A_N$ series catastrophes. We also propose methods for the calculation of a type $A_N$ catastrophe's parameters (the moment method and the maximum likelihood method), and their modifications applicable to the cases of multimodal and degenerate quasi-unimodal distributions. We provide the results of numeric experiments on constructing statistical catastrophe models for random processes.