The distribution of the minimum of a positive sample

Research output: Contribution to journalArticle

  • Authors:
  • Christopher S. Withers
  • Saralees Nadarajah

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.

Bibliographical metadata

Original languageEnglish
Pages (from-to)89-96
Number of pages8
JournalStatistics and Probability Letters
Volume151
Early online date8 Apr 2019
DOIs
Publication statusPublished - Aug 2019