The distribution of the minimum of a positive sample

Christopher S. Withers and Saralees Nadarajah

Statistics & Probability Letters, 2019, vol. 151, issue C, 89-96

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.

Keywords: Density; Maximum; Moments (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spl.2019.04.002

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