Maxima and sums of non-stationary random length sequences

Natalia M. Markovich; Igor V. Rodionov

doi:10.1007/s10687-020-00372-5

Maxima and sums of non-stationary random length sequences

Natalia M. Markovich
, Igor V. Rodionov

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

9 Scopus citations

Abstract

We study non-stationary random length sequences of random variables with regularly varying tails. Tail and extremal indexes of their maxima and linear combinations are found. We obtain conditions when both sums and maxima of these sequences have the same tail and extremal indexes. Their extremal index corresponds to the tail index of the most heavy-tailed random variable in the sequence.

Original language	English
Pages (from-to)	451-464
Number of pages	14
Journal	Extremes
Volume	23
Issue number	3
DOIs	https://doi.org/10.1007/s10687-020-00372-5
State	Published - 1 Sep 2020
Externally published	Yes

Keywords

Extremal index
Non-stationarity
Random length sequences
Regularly varying tail
Tail index

ASJC Scopus subject areas

Statistics and Probability
Engineering (miscellaneous)
Economics, Econometrics and Finance (miscellaneous)

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10.1007/s10687-020-00372-5

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abstract = "We study non-stationary random length sequences of random variables with regularly varying tails. Tail and extremal indexes of their maxima and linear combinations are found. We obtain conditions when both sums and maxima of these sequences have the same tail and extremal indexes. Their extremal index corresponds to the tail index of the most heavy-tailed random variable in the sequence.",

keywords = "Extremal index, Non-stationarity, Random length sequences, Regularly varying tail, Tail index",

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AU - Rodionov, Igor V.

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N2 - We study non-stationary random length sequences of random variables with regularly varying tails. Tail and extremal indexes of their maxima and linear combinations are found. We obtain conditions when both sums and maxima of these sequences have the same tail and extremal indexes. Their extremal index corresponds to the tail index of the most heavy-tailed random variable in the sequence.

AB - We study non-stationary random length sequences of random variables with regularly varying tails. Tail and extremal indexes of their maxima and linear combinations are found. We obtain conditions when both sums and maxima of these sequences have the same tail and extremal indexes. Their extremal index corresponds to the tail index of the most heavy-tailed random variable in the sequence.

KW - Extremal index

KW - Non-stationarity

KW - Random length sequences

KW - Regularly varying tail

KW - Tail index

UR - https://www.scopus.com/pages/publications/85082864594

U2 - 10.1007/s10687-020-00372-5

DO - 10.1007/s10687-020-00372-5

M3 - Article

AN - SCOPUS:85082864594

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VL - 23

SP - 451

EP - 464

JO - Extremes

JF - Extremes

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ER -

Maxima and sums of non-stationary random length sequences

Abstract

Keywords

ASJC Scopus subject areas

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