Probabilities for the size of largest clusters and smallest intervals

Sylvan R. Wallenstein, Joseph Naus

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

Given N points distributed at random on [0, 1), let npbe the size of the largest number of points clustered within an interval of length p. Previous work finds Pr (np≥ n), for n > N/2, and for n ≤ N/2, p=1/L, L an integer. The formula for the case p=1/L is in terms of the sum of L×L determinants and is not computationally feasible for large L. The present paper derives such a computational formula.

Original languageEnglish (US)
Pages (from-to)690-697
Number of pages8
JournalJournal of the American Statistical Association
Volume69
Issue number347
DOIs
StatePublished - Jan 1 1974

Fingerprint

Interval
Determinant
Integer

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

@article{435acf81f63e4ab492b86bb0c24dda93,
title = "Probabilities for the size of largest clusters and smallest intervals",
abstract = "Given N points distributed at random on [0, 1), let npbe the size of the largest number of points clustered within an interval of length p. Previous work finds Pr (np≥ n), for n > N/2, and for n ≤ N/2, p=1/L, L an integer. The formula for the case p=1/L is in terms of the sum of L×L determinants and is not computationally feasible for large L. The present paper derives such a computational formula.",
author = "Wallenstein, {Sylvan R.} and Joseph Naus",
year = "1974",
month = "1",
day = "1",
doi = "https://doi.org/10.1080/01621459.1974.10480190",
language = "English (US)",
volume = "69",
pages = "690--697",
journal = "Journal of the American Statistical Association",
issn = "0162-1459",
publisher = "Taylor and Francis Ltd.",
number = "347",

}

Probabilities for the size of largest clusters and smallest intervals. / Wallenstein, Sylvan R.; Naus, Joseph.

In: Journal of the American Statistical Association, Vol. 69, No. 347, 01.01.1974, p. 690-697.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Probabilities for the size of largest clusters and smallest intervals

AU - Wallenstein, Sylvan R.

AU - Naus, Joseph

PY - 1974/1/1

Y1 - 1974/1/1

N2 - Given N points distributed at random on [0, 1), let npbe the size of the largest number of points clustered within an interval of length p. Previous work finds Pr (np≥ n), for n > N/2, and for n ≤ N/2, p=1/L, L an integer. The formula for the case p=1/L is in terms of the sum of L×L determinants and is not computationally feasible for large L. The present paper derives such a computational formula.

AB - Given N points distributed at random on [0, 1), let npbe the size of the largest number of points clustered within an interval of length p. Previous work finds Pr (np≥ n), for n > N/2, and for n ≤ N/2, p=1/L, L an integer. The formula for the case p=1/L is in terms of the sum of L×L determinants and is not computationally feasible for large L. The present paper derives such a computational formula.

UR - http://www.scopus.com/inward/record.url?scp=0345856472&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0345856472&partnerID=8YFLogxK

U2 - https://doi.org/10.1080/01621459.1974.10480190

DO - https://doi.org/10.1080/01621459.1974.10480190

M3 - Article

VL - 69

SP - 690

EP - 697

JO - Journal of the American Statistical Association

JF - Journal of the American Statistical Association

SN - 0162-1459

IS - 347

ER -