Unimodality of the distribution of record statistics

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Let X1,X2,..., be a sequence of independent and identically distributed random variables with absolutely continuous distribution function F. For n ≥ 1, we denote the order statistics of X1,X2,...,Xn by X1,n ≤ ... Xn,n. Define L(1) = 1, L(n+1) = min{j: j > L(n), Xj > Xj-1,j-1}, and X(n) = XL(n),L(n), n ≥ 1. The sequence {X(n)} ({L(n)}) is called upper record statistics (times). In this article, we deal with unimodality of record statistics. We also deal with the strong unimodality of record statistics.

Original languageEnglish (US)
Pages (from-to)395-398
Number of pages4
JournalStatistics and Probability Letters
Volume56
Issue number4
DOIs
StatePublished - Feb 15 2002

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Record Statistics
Unimodality
Continuous Distributions
Absolutely Continuous
Order Statistics
Identically distributed
Continuous Function
Distribution Function
Random variable
Denote
Statistics

All Science Journal Classification (ASJC) codes

  • Statistics, Probability and Uncertainty
  • Statistics and Probability

Cite this

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title = "Unimodality of the distribution of record statistics",
abstract = "Let X1,X2,..., be a sequence of independent and identically distributed random variables with absolutely continuous distribution function F. For n ≥ 1, we denote the order statistics of X1,X2,...,Xn by X1,n ≤ ... Xn,n. Define L(1) = 1, L(n+1) = min{j: j > L(n), Xj > Xj-1,j-1}, and X(n) = XL(n),L(n), n ≥ 1. The sequence {X(n)} ({L(n)}) is called upper record statistics (times). In this article, we deal with unimodality of record statistics. We also deal with the strong unimodality of record statistics.",
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Unimodality of the distribution of record statistics. / Basak, Prasanta; Basak, Indrani.

In: Statistics and Probability Letters, Vol. 56, No. 4, 15.02.2002, p. 395-398.

Research output: Contribution to journalArticle

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AB - Let X1,X2,..., be a sequence of independent and identically distributed random variables with absolutely continuous distribution function F. For n ≥ 1, we denote the order statistics of X1,X2,...,Xn by X1,n ≤ ... Xn,n. Define L(1) = 1, L(n+1) = min{j: j > L(n), Xj > Xj-1,j-1}, and X(n) = XL(n),L(n), n ≥ 1. The sequence {X(n)} ({L(n)}) is called upper record statistics (times). In this article, we deal with unimodality of record statistics. We also deal with the strong unimodality of record statistics.

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