Moments and cumulants of the extremes of a sample from a uniform distribution

Christopher S. Withers; Saralees Nadarajah

doi:10.1016/j.spl.2018.10.006

Moments and cumulants of the extremes of a sample from a uniform distribution

Christopher S. Withers, Saralees Nadarajah^*

^*Corresponding author for this work

Industrial Research Limited of New Zealand

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

Abstract

We give expansions in inverse powers of the sample size [Formula presented] for the joint moments and cumulants of the extremes when sampling from a uniform distribution. Estimates of low bias are given for smooth functions of the end points and their performance illustrated by simulations. Some extensions are given for general bivariate extreme estimates.

Original language	English
Pages (from-to)	238-247
Number of pages	10
Journal	Statistics and Probability Letters
Volume	145
Early online date	11 Oct 2018
DOIs	https://doi.org/10.1016/j.spl.2018.10.006
Publication status	Published - 1 Feb 2019

Keywords

Edgeworth expansion
Order
Unbiasedness

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10.1016/j.spl.2018.10.006

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title = "Moments and cumulants of the extremes of a sample from a uniform distribution",

abstract = "We give expansions in inverse powers of the sample size [Formula presented] for the joint moments and cumulants of the extremes when sampling from a uniform distribution. Estimates of low bias are given for smooth functions of the end points and their performance illustrated by simulations. Some extensions are given for general bivariate extreme estimates.",

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AU - Nadarajah, Saralees

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N2 - We give expansions in inverse powers of the sample size [Formula presented] for the joint moments and cumulants of the extremes when sampling from a uniform distribution. Estimates of low bias are given for smooth functions of the end points and their performance illustrated by simulations. Some extensions are given for general bivariate extreme estimates.

AB - We give expansions in inverse powers of the sample size [Formula presented] for the joint moments and cumulants of the extremes when sampling from a uniform distribution. Estimates of low bias are given for smooth functions of the end points and their performance illustrated by simulations. Some extensions are given for general bivariate extreme estimates.

KW - Edgeworth expansion

KW - Order

KW - Unbiasedness

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U2 - 10.1016/j.spl.2018.10.006

DO - 10.1016/j.spl.2018.10.006

M3 - Article

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VL - 145

SP - 238

EP - 247

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

ER -

Moments and cumulants of the extremes of a sample from a uniform distribution

Abstract

Keywords

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