On the asymptotics of discrete order statistics

J. S. Athreya; S. Sethuraman

doi:10.1016/S0167-7152(01)00042-6

On the asymptotics of discrete order statistics

J. S. Athreya, S. Sethuraman

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

Let X₁, X₂,…, X_n be a sequence of independent, identically distributed positive integer random variables. We study the asymptotics of the likelihood that the sample maximum is achieved k times and in its spacing relative to the second highest value. Earlier and other results are discussed in context. Also, some investigation is made when the sample is Markovian. Different results emerge in this case.

Original language	English (US)
Pages (from-to)	243-249
Number of pages	7
Journal	Statistics and Probability Letters
Volume	54
Issue number	3
DOIs	https://doi.org/10.1016/S0167-7152(01)00042-6
State	Published - Oct 1 2001
Externally published	Yes

Keywords

Asymptotics
Extreme
Order statistics
Primary 62G32
Secondary 47F30
Uniqueness

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1016/S0167-7152(01)00042-6

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AB - Let X1, X2,…, Xn be a sequence of independent, identically distributed positive integer random variables. We study the asymptotics of the likelihood that the sample maximum is achieved k times and in its spacing relative to the second highest value. Earlier and other results are discussed in context. Also, some investigation is made when the sample is Markovian. Different results emerge in this case.

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KW - Extreme

KW - Order statistics

KW - Primary 62G32

KW - Secondary 47F30

KW - Uniqueness

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JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 3

ER -

On the asymptotics of discrete order statistics

Abstract

Keywords

ASJC Scopus subject areas

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