New characterization of discrete distributions through weak records

F. A. Aliev

doi:10.1137/tprbau000044000004000756000001

New characterization of discrete distributions through weak records

F. A. Aliev

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

10 Scopus citations

Abstract

Let X₁,X₂,... be a sequence of independent and identically distributed random variables taking on values 0, 1,... with a distribution function F such that F(n) < 1 for any n = 0, 1,... and EX₁ log(1 + X₁) < ∞. Let X_L(n) be the nth weak record value and {A_k}^∞_k=0 be any sequence of positive numbers, such that A_k+1 > A_k - 1. This paper shows that if there exists an F(x), with E{X_L(n+2) - X_L(n) = s} = A_s for some n > 0 and all s ≧ 0, then F(x) is unique.

Original language	English (US)
Pages (from-to)	756-761
Number of pages	6
Journal	Theory of Probability and its Applications
Volume	44
Issue number	4
DOIs	https://doi.org/10.1137/tprbau000044000004000756000001
State	Published - Dec 1999
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

Characterization of discrete distributions
Records
Weak records

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10.1137/tprbau000044000004000756000001

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title = "New characterization of discrete distributions through weak records",

abstract = "Let X1,X2,... be a sequence of independent and identically distributed random variables taking on values 0, 1,... with a distribution function F such that F(n) < 1 for any n = 0, 1,... and EX1 log(1 + X1) < ∞. Let XL(n) be the nth weak record value and {Ak}∞k=0 be any sequence of positive numbers, such that Ak+1 > Ak - 1. This paper shows that if there exists an F(x), with E{XL(n+2) - XL(n) = s} = As for some n > 0 and all s ≧ 0, then F(x) is unique.",

keywords = "Characterization of discrete distributions, Records, Weak records",

author = "Aliev, {F. A.}",

year = "1999",

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doi = "10.1137/tprbau000044000004000756000001",

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T1 - New characterization of discrete distributions through weak records

AU - Aliev, F. A.

PY - 1999/12

Y1 - 1999/12

N2 - Let X1,X2,... be a sequence of independent and identically distributed random variables taking on values 0, 1,... with a distribution function F such that F(n) < 1 for any n = 0, 1,... and EX1 log(1 + X1) < ∞. Let XL(n) be the nth weak record value and {Ak}∞k=0 be any sequence of positive numbers, such that Ak+1 > Ak - 1. This paper shows that if there exists an F(x), with E{XL(n+2) - XL(n) = s} = As for some n > 0 and all s ≧ 0, then F(x) is unique.

AB - Let X1,X2,... be a sequence of independent and identically distributed random variables taking on values 0, 1,... with a distribution function F such that F(n) < 1 for any n = 0, 1,... and EX1 log(1 + X1) < ∞. Let XL(n) be the nth weak record value and {Ak}∞k=0 be any sequence of positive numbers, such that Ak+1 > Ak - 1. This paper shows that if there exists an F(x), with E{XL(n+2) - XL(n) = s} = As for some n > 0 and all s ≧ 0, then F(x) is unique.

KW - Characterization of discrete distributions

KW - Records

KW - Weak records

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DO - 10.1137/tprbau000044000004000756000001

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AN - SCOPUS:0033622209

SN - 0040-585X

VL - 44

SP - 756

EP - 761

JO - Theory of Probability and its Applications

JF - Theory of Probability and its Applications

IS - 4

ER -

New characterization of discrete distributions through weak records

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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