The distribution of the minimum of a positive sample

Christopher S. Withers; Saralees Nadarajah

doi:10.1016/j.spl.2019.04.002

The distribution of the minimum of a positive sample

Christopher S. Withers, Saralees Nadarajah^*

^*Corresponding author for this work

Industrial Research Limited of New Zealand

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

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Abstract

We give expansions for the distribution function, density function and moments of the sample minimum when sampling from a distribution on 0,x ₂ that is nearly analytic at zero. Similar results are given for the sample maximum when sampling from a distribution on x ₁ ,x ₂ that is nearly analytic at x ₂ . When these distributions are analytic, the expansions are in inverse powers of the sample size n. If not, they require a double expansion.

Original language	English
Pages (from-to)	89-96
Number of pages	8
Journal	Statistics and Probability Letters
Volume	151
Early online date	8 Apr 2019
DOIs	https://doi.org/10.1016/j.spl.2019.04.002
Publication status	Published - Aug 2019

Keywords

Density
Maximum
Moments

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10.1016/j.spl.2019.04.002

kit225Accepted author manuscript, 193 KBLicence: CC BY-NC-ND

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AB - We give expansions for the distribution function, density function and moments of the sample minimum when sampling from a distribution on 0,x 2 that is nearly analytic at zero. Similar results are given for the sample maximum when sampling from a distribution on x 1 ,x 2 that is nearly analytic at x 2 . When these distributions are analytic, the expansions are in inverse powers of the sample size n. If not, they require a double expansion.

KW - Density

KW - Maximum

KW - Moments

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DO - 10.1016/j.spl.2019.04.002

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VL - 151

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EP - 96

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

ER -

The distribution of the minimum of a positive sample

Abstract

Keywords

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