×

Tests for the extreme value and Weibull distributions based on normalized spacings. (English) Zbl 0616.62057

Discussed in this article are tests for the extreme-value distribution, or, equivalently, for the two-parameter Weibull distribution when parameters are unknown and the sample may be censored. The three tests investigated are based on the median, the mean, and the Anderson-Darling \(A^ 2\) statistic calculated from a set \(z_ i\) of values derived from the spacings of the sample. The median and the mean have previously been discussed by N. R. Mann, E. M. Scheuer and K. W. Fertig [Commun. Stat. 2, 383-400 (1973; Zbl 0271.62127)] and by M. L. Tiku and M. Singh [Testing the two parameter Weibull distribution. Commun. Stat., Theory Methods A10, 907-918 (1981)].
Asymptotic distributions and points are given for the test statistics, based on recently developed theory, and power studies are conducted to compare them with each other and with two other statistics suitable for the test. Of the normalized spacings tests, \(A^ 2\) is recommended overall; the mean also gives good power in many situations, but can be nonconsistent.

MSC:

62G10 Nonparametric hypothesis testing

Citations:

Zbl 0271.62127
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Statistical Estimates and Transformed Beta Variables, Wiley, New York, 1958. · Zbl 0086.34501
[2] Chandra, Journal of the American Statistical Association 76 pp 729– (1981)
[3] and , Eds., Goodness-of-Fit Techniques, Marcel Dekker, New York, to appear, 1986.
[4] Gerlach, Mathematische Operationsforschung und Statistik, Series Statistics 10 pp 427– (1979)
[5] Littell, Communications in Statistics B, Simulation and Computation 3 pp 257– (1979)
[6] , and , ”Tests of Fit Based on Normalized Spacings.” Technical Report No. 369, Department of Statistics, Stanford University. · Zbl 0638.62037
[7] ”Results on Statistical Estimation and Hypothesis Testing with Application to the Weibull and Extreme- Value Distributions,” Aerospace Research Laboratories Report No. ARL 68-0068, Office of Aerospace Research, United States Air Force, Wright-Patterson Air Force Base, Ohio, 1968.
[8] Mann, Technometrics 17 pp 237– (1975)
[9] , and , ”Confidence and Tolerance Bounds and a New Goodness-of-Fit Test for the Two-Parameter Weibull or Extreme-Value Distributions (with Tables for Censored Samples of Size 3(1)25),” Aerospace Research Laboratories Report No. ARL 71-0077, Air Force Systems Command, United States Air Force, Wright-Patterson Air Force Base, Ohio, 1971.
[10] Mann, Communications in Statistics 2 pp 383– (1973)
[11] Smith, Communications in Statistics A, Theory and Methods 5 pp 119– (1976)
[12] Stephens, Journal of the American Statistical Association 69 pp 730– (1974)
[13] Stephens, Biometrika 64 pp 583– (1977)
[14] Tiku, Communications in Statistics, A 10 pp 907– (1981)
[15] Pyke, Journal of the Royal Statistical Society, B 27 pp 395– (1965)
[16] White, Technometrics 11 pp 373– (1969)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.