The Calculation of the Density and Distribution Functions of Strictly Stable Laws

Viacheslav Saenko
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Viacheslav Saenko: Department of Theoretical Physics, Ulyanovsk State University, 432970 Ulyanovsk, Russia

Mathematics, 2020, vol. 8, issue 5, 1-38

Abstract: Integral representations for the probability density and distribution function of a strictly stable law with the characteristic function in the Zolotarev’s “C” parametrization were obtained in the paper. The obtained integral representations express the probability density and distribution function of standard strictly stable laws through a definite integral. Using the methods of numerical integration, the obtained integral representations allow us to calculate the probability density and distribution function of a strictly stable law for a wide range of admissible values of parameters ( α , θ ) . A number of cases were given when numerical algorithms had difficulty in calculating the density. Formulas were given to calculate the density and distribution function with an arbitrary value of the scale parameter λ .

Keywords: stable distribution; probability density function; distribution function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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