Expansions for the Distribution of the Maximum from Distributions with a Power Tail when a Trend is Present

Christopher S. Withers and Saralees Nadarajah ()
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Christopher S. Withers: Industrial Research Limited
Saralees Nadarajah: University of Manchester

Methodology and Computing in Applied Probability, 2013, vol. 15, issue 3, 525-546

Abstract: Abstract We give expansions about the second type of extreme value (EV2 or Fréchet) distribution in inverse powers of the sample size, n + 1, for the sample maximum M n when the jth observation is μ(j/n) + e j , μ(·) is any smooth trend function and the residuals e 0, ..., e n are independent with a common Pareto type distribution. We show that the distribution of the maximum has a triple expansion in inverse powers of n. We give the likelihood for this case and illustrate its practical value using simulated and real data sets.

Keywords: Bell polynomials; Expansions; Extreme value distribution; Maximum; Power tails; Trend; Primary 62E15; Secondary 62E17 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s11009-011-9264-5

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