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

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  • Christopher S. Withers

    (Industrial Research Limited)

  • Saralees Nadarajah

    (University of Manchester)

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.

Suggested Citation

  • Christopher S. Withers & Saralees Nadarajah, 2013. "Expansions for the Distribution of the Maximum from Distributions with a Power Tail when a Trend is Present," Methodology and Computing in Applied Probability, Springer, vol. 15(3), pages 525-546, September.
    • Handle: RePEc:spr:metcap:v:15:y:2013:i:3:d:10.1007_s11009-011-9264-5
    DOI: 10.1007/s11009-011-9264-5
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    References listed on IDEAS

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    1. S. Nadarajah & J. Shiau, 2005. "Analysis of Extreme Flood Events for the Pachang River, Taiwan," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 19(4), pages 363-374, August.
    2. Leipala, Timo, 1978. "On the solutions of stochastic traveling salesman problems," European Journal of Operational Research, Elsevier, vol. 2(4), pages 291-297, July.
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