Geodesic
Application of catastrophe theory for
Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 3, pp. 485-502

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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.
Mots-clés : multimodal distributions
Keywords: catastrophe theory, parametric families of functions, moment method, maximum likelihood methodю. 
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     author = {S. Glukhova and E. A. Palkin},
     title = {Application of catastrophe theory for},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {485--502},
     publisher = {mathdoc},
     volume = {49},
     number = {3},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2004_49_3_a3/}
}
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S. Glukhova; E. A. Palkin. Application of catastrophe theory for. Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 3, pp. 485-502. http://geodesic.mathdoc.fr/item/TVP_2004_49_3_a3/