Distribution tails of sample quantiles and subexponentiality

Michael Braverman; Gennady Samorodnitsky

doi:10.1016/S0304-4149(98)00022-2

Distribution tails of sample quantiles and subexponentiality

Michael Braverman, Gennady Samorodnitsky

Department of Mathematics

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

Abstract

We show that subexponentiality is not sufficient to guarantee that the distribution tail of a sample quantile of an infinitely divisible process is equivalent to the "tail" of the same sample quantile under the corresponding Lévy measure. However, such an equivalence result is shown to hold under either an assumption of an appropriately slow tail decay or an assumption on the structure of the process.

Original language	English
Pages (from-to)	45-60
Number of pages	16
Journal	Stochastic Processes and their Applications
Volume	76
Issue number	1
DOIs	https://doi.org/10.1016/S0304-4149(98)00022-2
State	Published - 1 Aug 1998

Keywords

60G70
Infinitely divisible processes
Lévy measure
Primary 60G17
Sample quantiles
Secondary 60E07
Subexponential distribution
Tail behavior

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Applied Mathematics

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10.1016/S0304-4149(98)00022-2

Cite this

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AU - Samorodnitsky, Gennady

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N2 - We show that subexponentiality is not sufficient to guarantee that the distribution tail of a sample quantile of an infinitely divisible process is equivalent to the "tail" of the same sample quantile under the corresponding Lévy measure. However, such an equivalence result is shown to hold under either an assumption of an appropriately slow tail decay or an assumption on the structure of the process.

AB - We show that subexponentiality is not sufficient to guarantee that the distribution tail of a sample quantile of an infinitely divisible process is equivalent to the "tail" of the same sample quantile under the corresponding Lévy measure. However, such an equivalence result is shown to hold under either an assumption of an appropriately slow tail decay or an assumption on the structure of the process.

KW - 60G70

KW - Infinitely divisible processes

KW - Lévy measure

KW - Primary 60G17

KW - Sample quantiles

KW - Secondary 60E07

KW - Subexponential distribution

KW - Tail behavior

UR - https://www.scopus.com/pages/publications/0039500436

U2 - 10.1016/S0304-4149(98)00022-2

DO - 10.1016/S0304-4149(98)00022-2

M3 - Article

AN - SCOPUS:0039500436

SN - 0304-4149

VL - 76

SP - 45

EP - 60

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 1

ER -

Distribution tails of sample quantiles and subexponentiality

Abstract

Keywords

ASJC Scopus subject areas

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