Stability of decomposition into components of a discontinuous distribution function in uniform metric
type: Item
instance of: scholarly article
title: Stability of decomposition into components of a discontinuous distribution function in uniform metric
zbMATH Open document ID: 0847.60014
DOI: 10.1007/BF02337758
published in: Lithuanian Mathematical Journal
publication date: 1996-02-25T00:00:00Z
review text: The first part is devoted to the characterization of various concepts of convergence of d.f.'s of real valued r.v.'s. The main attention is paid to the uniform convergence (on \(\mathbb{R})\) of d.f.'s (i.e. to convergence in the metric \(\rho)\) and to the strong convergence. The second part provides conditions for strong precompactness of a family of d.f.'s. In the third section the extension of previous results to bounded increasing functions is given. The final part deals with \(\rho\)-convergence \(\rho (F_n, F) \to 0\) \((n \to \infty)\) of convolutions \(F_n = F_{n1} * F_{n2}\) when \(F\) has at least one jump. As a corollary necessary and sufficient conditions are found for strong convergence of d.f.'s of \(\xi_{n,1} + \cdots + \xi_{n, k_n} - A_n\) to the Poisson d.f. with parameter \(\lambda > 0\) (here \(\xi_{n,1}, \dots, \xi_{n, k_n}\) are independent r.v.'s, \(A_n = \text{const})\).
Mathematics Subject Classification ID: 60Fxx
Mathematics Subject Classification ID: 60E05
zbMATH DE Number: 846598
zbMATH Keywords: characterization of various concepts of convergence
zbMATH Keywords: uniform convergence
zbMATH Keywords: conditions of strong precompactness
zbMATH Keywords: strong convergence
author: J. J. Mačys
reviewed by: Alexander V. Bulinski
MaRDI profile type: Publication
cites work: Q5829358
cites work: Q3339832
cites work: Q4056767
cites work: Q5644548
full work available at URL: https://doi.org/10.1007/bf02337758
OpenAlex ID: W1979827320
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description: scientific article; zbMATH DE number 846598