Number of points of discontinuity of concentration functions

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1984 English Publisher:Springer Science and Business Media LLCJournal:Mathematical Notes of the Academy of Sciences of the USSR, volume 35, pages 72-73 (issn: 0001-4346, eissn: 1573-8876,

Copyright policy )

Authors: Anan'evskij, S. M.;

doi: 10.1007/bf01142299

Number of points of discontinuity of concentration functions

- Summary
- Subjects
- Metrics

Abstract

Let X be a random variable that takes a finite number of values, say n, Q the concentration function of X extended for negative values by zero, and N(X,n) the number of discontinuity points of Q. Then \(N(X,n)=n\) for \(n\leq 2\), 3\(\leq N(X,3)\leq 4\), \(4\leq N(X,n)\leq n(n-1)/2+1\) for \(n\geq 4\), and all estimates are sharp.

Related Organizations

St Petersburg University
Russian Federation
Pushkin Leningrad State University
Russian Federation

Keywords

number of discontinuity points, concentration function, Distribution theory

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	0
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average

Found an issue? Give us feedback

0

Average

Fields of Science

Fields of Science

Upload OA version

Are you the author of this publication? Upload your Open Access version to Zenodo!

It’s fast and easy, just two clicks!

uploadUpload now