Abstract
Estimation procedures for parameters of the Frechet and the three-parameter Weibull distribution are reviewed, after the relationships between these two distributions and the Gumbel distribution are discussed. Included in the review are maximum-likelihood and moment estimators as well as linearly based estimators and some that are extremely simple, involving only a few order statistics. Large- and small-sample properties are discussed.
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References
Bain, L.J., 1972, Technometrics 14, pp. 831–840.
Cohen, A.C., Jr. and Witten, B.J., 1982. Commun. in Statist. 11, pp. 2631–2656.
Cramér, H., 1946, Mathematcat Method’s of statbstics. Princeton University Press, Princeton, N.J.
Dubey, S.D., 1966, Naval Res. Logist. Quart. 13, pp. 253–263.
Dubey, S.D., 1966, Naval Res. Logist. Quart. 14, pp. 261–267.
Epstein, B. and Sobel, M., 1954, Ann. Math. Statist. 25, pp. 373–381.
Fisher, R.A. and Tippett, L.H.C., 1928, Proc. Camb. Philos. Soc. 24, pp. 180–190.
Gnedenko, B.V., 1943, Ann. Math. 44, pp. 423–453.
Gumbel, E.J., 1954, Statbsticat Theony ab Extteme Va,Luu and Some Pnac Lca. App.p.Lcation. A Se Aim ob Lectwtm National Bureau of Standards Applied Mathematics Series, 33, U.S. Government Printing Office, Washington, D.C.
Harter, H.L. and Dubey, S.D., 1967, Aerospace Research Labonaton,í.ez Repont ARL 67–0059, Office of Aerospace Research, Wright-Patterson A.F.Base, Ohio.
Harter, H.L. and Moore, A.H., 1965, Technometrics, 7, pp. 639–643.
Jenkinson, A.F., 1955, Quart. J. Royal Meteor. Soc. 33, pp. 349–363.
Kao, J.H.K., 1959, Technometrics 1, pp. 389–407.
Kappenman, R.F., 1981, J. Statist. Comput. Simul. 13, pp. 245–254.
Laue, R.V., 1974, Unpublished paper, Bell Laboratories, Holmdel, N.J.
Lemon, G.H., 1975, Technometrics 17, pp. 247–254.
Mann, N.R., 1967, Technometrics 9, pp. 629–645.
Mann, N.R., Schafer, R.E. and Singpurwalla, N.D., 1974, Method’s bon StatiztLcaL Ana.y4Lo ob Rdiabit ty and Labe Data, John Wiley, New York.
Mann, N.R. and Singpurwalla, N.D., 1982, in Encyclopedia of Statsticaes Ciencea, Eds. S. Kotz, N.L. Johnson and C.B. Read, Vol 2, pp. 606–613.
Tiago de Oliveira, J., 1983, Unpublished paper.
Weibull, W., 1951, J. Appl. Mechanics 18, pp. 293–297.
Weissman, I., 1978, J. Amer. Statist. Assoc. 73, pp. 812–815.
Wyckoff, J., Bain, L.J. and Engelhardt, M.D., 1980, J. Statist. Comput. Simul. 11, pp. 139–151.
Woodroofe, M., 1974, Ann. Statist. 2, pp. 474–488.
Yegulalp, T.M. and Kuo, J.T., 1974, Bull. Seism. Soc. Amer. 64, pp. 393–414.
Zanakis, S.H., 1979, J. Statist. Comput. Simul. 9, pp. 101–116.
Zanakis, S.H. and Mann, N.R., 1982, Naval Res. Logist. Quart. 29, pp. 419–428.
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Mann, N.R. (1984). Statistical Estimation of Parameters of the Weibull and Frechet Distributions. In: de Oliveira, J.T. (eds) Statistical Extremes and Applications. NATO ASI Series, vol 131. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3069-3_6
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DOI: https://doi.org/10.1007/978-94-017-3069-3_6
Publisher Name: Springer, Dordrecht
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