FREQUENCY DISTRIBUTIONS IN BIOINFORMATICS: THE DEVELOPMENT

Authors

  • J. Astola Academician of the Academy of Science of Finland
  • E. A. Danielian Chair of Probability Theory and Mathematical Statistics, YSU
  • S. K. Arzumanyan Chair of Probability Theory and Mathematical Statistics, YSU

DOI:

https://doi.org/10.46991/PYSU:A/2010.44.3.003

Keywords:

frequency distributbiomion, olecular sequence, regular variation, convexity, stability by parameters, asymptotic expansion

Abstract

The mathematical investigation of large-scale biomolecular sequences is being carried out by analyzing the properties of events arising in such sequences. This survey is devoted to discussion of results in this field. Based on general empirical facts being fulfilled for all frequency distributions, we discuss the axiomatics suggested by J. Astola and E. Danielyan. The axiomatics postulates the regular variation of frequency distribution with asymptotically constant slowly varying component, the form of its shape, and the stability by parameters. The verification of the axiomatics fulfillment for wellknown frequency distributions is done. The paper describes also methods of construction of new parametric families of frequency distributions. These methods are: usage of stationary distributions of birth-death process, special functions, stable densities, etc. The problem of stability by parameters is formulated the results on stability by parameters in terms of various classical metrics are given. The conditions of regular variation for different families of frequency distributions are formulated.

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Published

2010-10-21

How to Cite

Astola, J., Danielian, E. A., & Arzumanyan, S. K. . (2010). FREQUENCY DISTRIBUTIONS IN BIOINFORMATICS: THE DEVELOPMENT. Proceedings of the YSU A: Physical and Mathematical Sciences, 44(3 (223), 3–22. https://doi.org/10.46991/PYSU:A/2010.44.3.003

Issue

Section

Mathematics