March 3, 2026

Estimation of the Remainder Term in the Expansion of the Stable Law for Extreme Values of the Asymmetry Parameter

Key Points

The analysis shows the validity of asymptotic expansions for the probability density and distribution functions.
Residual terms are estimated, indicating their significance in the context of the expansions' accuracy.
Calculations confirm applicable coordinate regions for the asymptotic expansions, enhancing their utility.
The approach involves examining the stable law's behavior as it relates to extreme asymmetry parameters.

Abstract

This paper examines the expansion of the strictly stable law for x 0 and x in the case of extreme values of the asymmetry parameter. Asymptotic expansions of the probability density and distribution functions are obtained, as are estimates of the residual terms of these expansions. Based on the estimates of the residual terms, a criterion is presented that makes it possible to determine the coordinate region within which it is possible to use these asymptotic expansions. The calculations confirm the validity of the expressions.

Bookmark

Estimation of the Remainder Term in the Expansion of the Stable Law for Extreme Values of the Asymmetry Parameter

Key Points

Abstract

Cite This Study