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

Viacheslav V. Saenko ()
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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

Mathematics, 2022, vol. 10, issue 20, 1-27

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.

Keywords: stable distribution; expansion of the stable distribution; calculation of the stable distribution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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