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.
Keywords:multimodal distributions, catastrophe theory, parametric families of functions, moment method, maximum likelihood methodž.