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The Calculation of the Probability Density and Distribution Function of a Strictly Stable Law in the Vicinity of Zero

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  • Viacheslav V. Saenko

    (S.P. Kapitsa Scientific Research Institute of Technology, Ulyanovsk State University, 42, L. Tolstoy St., 432017 Ulyanovsk, Russia)

Abstract

The problem of calculating the probability density and distribution function of a strictly stable law is considered at x → 0 . The expansions of these values into power series were obtained to solve this problem. It was shown that in the case α < 1 , the obtained series were asymptotic at x → 0 ; in the case α > 1 , they were convergent; and in the case α = 1 in the domain | x | < 1 , these series converged to an asymmetric Cauchy distribution. It has been shown that at x → 0 the obtained expansions can be successfully used to calculate the probability density and distribution function of strictly stable laws.

Suggested Citation

  • Viacheslav V. Saenko, 2022. "The Calculation of the Probability Density and Distribution Function of a Strictly Stable Law in the Vicinity of Zero," Mathematics, MDPI, vol. 10(20), pages 1-27, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3861-:d:945634
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    References listed on IDEAS

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    1. Viacheslav Saenko, 2020. "The Calculation of the Density and Distribution Functions of Strictly Stable Laws," Mathematics, MDPI, vol. 8(5), pages 1-38, May.
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