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An optimum t‐test for the scale parameter of an extreme‐value distribution

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  • Lai K. Chan
  • S. W. H. Cheng
  • E. R. Mead

Abstract

A Student's t‐test proposed by Ogawa is considered for the hypothesis Ho: σ=σo against the alternative hypothesis H1: σ ≠ σo, where σ is the scale parameter of the Extremevalue distribution of smallest values with known location parameter μ. The test is based on a few sample quantiles chosen from a large sample so as to give asymptotically maximum power to the test when the number of sample quantiles is fixed. A table which facilitates the computation of the test statistic is given. Several schemes for determining the ranks of the sample quantiles by the optimal spacings are compared and the effect of the bias of the estimate of σ on the test is investigated through a Monte Carlo study.

Suggested Citation

  • Lai K. Chan & S. W. H. Cheng & E. R. Mead, 1972. "An optimum t‐test for the scale parameter of an extreme‐value distribution," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 19(4), pages 715-723, December.
    • Handle: RePEc:wly:navlog:v:19:y:1972:i:4:p:715-723
    DOI: 10.1002/nav.3800190412
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