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The distribution of the minimum of a positive sample

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  • Withers, Christopher S.
  • Nadarajah, Saralees

Abstract

We give expansions for the distribution function, density function and moments of the sample minimum when sampling from a distribution on 0,x2 that is nearly analytic at zero. Similar results are given for the sample maximum when sampling from a distribution on x1,x2 that is nearly analytic at x2. When these distributions are analytic, the expansions are in inverse powers of the sample size n. If not, they require a double expansion.

Suggested Citation

  • Withers, Christopher S. & Nadarajah, Saralees, 2019. "The distribution of the minimum of a positive sample," Statistics & Probability Letters, Elsevier, vol. 151(C), pages 89-96.
    • Handle: RePEc:eee:stapro:v:151:y:2019:i:c:p:89-96
    DOI: 10.1016/j.spl.2019.04.002
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    References listed on IDEAS

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    1. Balakrishnan, Narayanaswamy & Selvitella, Alessandro, 2017. "Symmetry of a distribution via symmetry of order statistics," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 367-372.
    2. Kim, Bara & Kim, Jeongsim & Lee, Sungji, 2018. "Strong unimodality of discrete order statistics," Statistics & Probability Letters, Elsevier, vol. 140(C), pages 48-52.
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    More about this item

    Keywords

    Density; Maximum; Moments;
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