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

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.