Aleškevičienė, A. K.; Statulevičius, V. A. Inversion formulas in the case of a discontinuous limit law. (English. Russian original) Zbl 0912.60038 Theory Probab. Appl. 42, No. 1, 1-16 (1997); translation from Teor. Veroyatn. Primen. 42, No. 1, 3-20 (1997). Let \(G\) be a function of bounded variation defined on \(\mathbb{R}\) with a set of discontinuity points \(A_G=\{\ldots,x_{-2},x_{-1},x_0,x_1,x_2,\ldots\}\) and let \(F\) be a distribution function on \(\mathbb{R},\) the set of discontinuity points \(A_F\) of which satisfies the condition \( A_F\supseteq A_G\cap \big\{ x: x_{\min}\leq x\leq x_{\max}\big\},\) where \(x_{\min}\) is the largest of the numbers \(x\) for which \(F(x)=0\) and \(x_{\max}\) is the smallest \(x,\) for which \(F(x+0)=1\). The authors estimate the distance in a uniform metric between \(F\) and \(G\) by means of the difference of their Fourier-Stieltjes transforms and the concentration of the functions \(F\) and \(G\) in the neighbourhood of discontinuity points. Reviewer: K.Kubilius (Vilnius) MSC: 60E15 Inequalities; stochastic orderings 60F99 Limit theorems in probability theory Keywords:inversion formula; distribution function; characteristic function; concentration function PDFBibTeX XMLCite \textit{A. K. Aleškevičienė} and \textit{V. A. Statulevičius}, Teor. Veroyatn. Primen. 42, No. 1, 3--20 (1997; Zbl 0912.60038); translation from Teor. Veroyatn. Primen. 42, No. 1, 3--20 (1997) Full Text: DOI Link