메뉴 건너뛰기




Volumn 7, Issue 4, 2004, Pages 291-307

Bayesian inference for extremes: Accounting for the three extremal types

Author keywords

Extremal types theorem; Extreme value theory; Generalized extreme value distribution; Poisson process; Reversible jump Markov chain Monte Carlo

Indexed keywords


EID: 26444468064     PISSN: 13861999     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10687-004-3479-6     Document Type: Article
Times cited : (56)

References (39)
  • 1
    • 5544256981 scopus 로고
    • Transformation of survival data to an extreme value distribution
    • Achcar, A.J., Bolfarine, H. and Pericchi, L.R., "Transformation of survival data to an extreme value distribution," Statistician 36, 229-234, (1987).
    • (1987) Statistician , vol.36 , pp. 229-234
    • Achcar, A.J.1    Bolfarine, H.2    Pericchi, L.R.3
  • 2
    • 5544275799 scopus 로고
    • Bayesian estimation of the parameters of the extreme value distribution
    • Ashour, S.K. and El-Adl, Y.M., "Bayesian estimation of the parameters of the extreme value distribution," Egypt. Stat. J. 24, 140-152, (1980).
    • (1980) Egypt. Stat. J. , vol.24 , pp. 140-152
    • Ashour, S.K.1    El-Adl, Y.M.2
  • 3
    • 23444461724 scopus 로고    scopus 로고
    • Bayesian analysis of extreme values by mixture modelling
    • Bottolo, P., Consonni, G., Dellaportas, P. and Lijoi, A., "Bayesian analysis of extreme values by mixture modelling," Extremes 6, 25-48, (2003).
    • (2003) Extremes , vol.6 , pp. 25-48
    • Bottolo, P.1    Consonni, G.2    Dellaportas, P.3    Lijoi, A.4
  • 4
    • 0345099641 scopus 로고
    • Convergence rates for the ultimate and penultimate approximations in extreme-value theory
    • Cohen, J.P., "Convergence rates for the ultimate and penultimate approximations in extreme-value theory," Adv. Appl. Probab. 14, 833-854, (1982a).
    • (1982) Adv. Appl. Probab. , vol.14 , pp. 833-854
    • Cohen, J.P.1
  • 5
    • 0012901863 scopus 로고
    • The penultimate form of approximation to normal extremes
    • Cohen, J.P., "The penultimate form of approximation to normal extremes," Adv. Appl. Probab. 14, 324-339, (1982b).
    • (1982) Adv. Appl. Probab. , vol.14 , pp. 324-339
    • Cohen, J.P.1
  • 7
    • 0030560555 scopus 로고    scopus 로고
    • Bayesian methods in extreme value modelling: A review and new developments
    • Coles, S.G. and Powell, E.A., "Bayesian methods in extreme value modelling: a review and new developments," Int. Star. Rev. 64, 119-136, (1996).
    • (1996) Int. Star. Rev. , vol.64 , pp. 119-136
    • Coles, S.G.1    Powell, E.A.2
  • 9
    • 0039607949 scopus 로고    scopus 로고
    • A Bayesian analysis of extreme rainfall data
    • Coles, S.G. and Tawn, J.A., "A Bayesian analysis of extreme rainfall data," Appl. Stat. 45, 463-478, (1996).
    • (1996) Appl. Stat. , vol.45 , pp. 463-478
    • Coles, S.G.1    Tawn, J.A.2
  • 10
    • 0000617024 scopus 로고
    • Models for exceedances over high thresholds
    • Davison, A.C. and Smith, R.L., "Models for exceedances over high thresholds," J. R. Stat. Soc., B 52, 393-442, (1990).
    • (1990) J. R. Stat. Soc., B , vol.52 , pp. 393-442
    • Davison, A.C.1    Smith, R.L.2
  • 11
    • 0001591373 scopus 로고
    • On the estimation of the extreme-value index and large quantile estimation
    • Dekkers, A.L.M. and de Haan, L., "On the estimation of the extreme-value index and large quantile estimation," Ann. Stat. 17, 1795-1832, (1989).
    • (1989) Ann. Stat. , vol.17 , pp. 1795-1832
    • Dekkers, A.L.M.1    De Haan, L.2
  • 12
    • 0027087815 scopus 로고
    • Trends in U.K. extreme sea levels: A spatial approach
    • Dixon, M.J. and Tawn, J.A., "Trends in U.K. extreme sea levels: a spatial approach," Geophys. J. Int. 111, 607-616, (1992).
    • (1992) Geophys. J. Int. , vol.111 , pp. 607-616
    • Dixon, M.J.1    Tawn, J.A.2
  • 13
    • 38249009021 scopus 로고
    • On predictive distribution functions for the three asymptotic extreme value distributions
    • Engelund, S. and Rackwitz, R., "On predictive distribution functions for the three asymptotic extreme value distributions," Struct. Saf. 11, 255-258, (1992).
    • (1992) Struct. Saf. , vol.11 , pp. 255-258
    • Engelund, S.1    Rackwitz, R.2
  • 14
    • 84958156266 scopus 로고
    • Limiting forms of frequency distributions of the largest or smallest member of a sample
    • Fisher, R.A. and Tippett, L.H.C., "Limiting forms of frequency distributions of the largest or smallest member of a sample," Proc. Camb. Philos. Soc. 24, 180-190, (1928).
    • (1928) Proc. Camb. Philos. Soc. , vol.24 , pp. 180-190
    • Fisher, R.A.1    Tippett, L.H.C.2
  • 15
    • 26444572901 scopus 로고
    • An statistical test for extreme value distributions
    • Coll. Math. Soc. Janos. Bolyai, Budapest
    • Galambos, J., "An statistical test for extreme value distributions," Tech. Rep. 32, Coll. Math. Soc. Janos. Bolyai, Budapest, 1980.
    • (1980) Tech. Rep. , vol.32
    • Galambos, J.1
  • 16
    • 0021518209 scopus 로고
    • Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images
    • Geman, S. and Geman, D., "Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images," IEEE Trans. Pattern Anal. Mach. Intell. 6, 721-741, (1984).
    • (1984) IEEE Trans. Pattern Anal. Mach. Intell. , vol.6 , pp. 721-741
    • Geman, S.1    Geman, D.2
  • 17
    • 26444617314 scopus 로고
    • A note on statistical choice of extremal models
    • Act. IX Jorn. Matem. Hispano-Lusas, Salamanca, II
    • Gomes, M.I., "A note on statistical choice of extremal models," Tech. Rep., Act. IX Jorn. Matem. Hispano-Lusas, Salamanca, II, 1982.
    • (1982) Tech. Rep.
    • Gomes, M.I.1
  • 18
    • 77956889087 scopus 로고
    • Reversible jump MCMC computation and Bayesian model determination
    • Green, P.J., "Reversible jump MCMC computation and Bayesian model determination," Biometrica 82, 711-732, (1995).
    • (1995) Biometrica , vol.82 , pp. 711-732
    • Green, P.J.1
  • 20
    • 77956890234 scopus 로고
    • Monte Carlo sampling methods using markov chains and their applications
    • Hastings, W.K., "Monte Carlo sampling methods using markov chains and their applications," Biometrica 57, 97-109, (1970).
    • (1970) Biometrica , vol.57 , pp. 97-109
    • Hastings, W.K.1
  • 21
    • 0042513218 scopus 로고
    • Testing whether the shape parameter is zero in the generalized extreme-value distribution
    • Hosking, J.R.M., "Testing whether the shape parameter is zero in the generalized extreme-value distribution," Biometrika 71, 367-374, (1984).
    • (1984) Biometrika , vol.71 , pp. 367-374
    • Hosking, J.R.M.1
  • 22
    • 84904261422 scopus 로고
    • The frequency distribution of the annual maximum (or minimum) of meteorological elements
    • Jenkinson, A.F., "The frequency distribution of the annual maximum (or minimum) of meteorological elements," Quant. J. R. Met. Soc. 81, 158-171, (1955).
    • (1955) Quant. J. R. Met. Soc. , vol.81 , pp. 158-171
    • Jenkinson, A.F.1
  • 24
    • 84980189014 scopus 로고
    • Bayesian prediction regions for the extreme order statistics
    • Lingappaiah, G.S., "Bayesian prediction regions for the extreme order statistics," Biom. J. 26, 49-56, (1984).
    • (1984) Biom. J. , vol.26 , pp. 49-56
    • Lingappaiah, G.S.1
  • 25
    • 0002276858 scopus 로고
    • The two-dimensional Poisson process and extremal processes
    • Pickands, J., "The two-dimensional Poisson process and extremal processes," J. Appl. Probab. 8, 745-756, (1971).
    • (1971) J. Appl. Probab. , vol.8 , pp. 745-756
    • Pickands, J.1
  • 26
    • 0001075431 scopus 로고
    • Statistical inference using extreme order statistics
    • Pickands, J., "Statistical inference using extreme order statistics," Ann. Stat. 3, 119-131, (1975).
    • (1975) Ann. Stat. , vol.3 , pp. 119-131
    • Pickands, J.1
  • 27
    • 0005396594 scopus 로고
    • Bayes quantile estimation and threshold selection for the generalized pareto family
    • (J. Galambos, S. Leigh, and E. Simiu, eds), Kluwer, Amsterdam
    • Pickands, J., "Bayes quantile estimation and threshold selection for the generalized pareto family," in Extreme Value Theory and Applications (J. Galambos, S. Leigh, and E. Simiu, eds), Kluwer, Amsterdam, 123-138, 1994.
    • (1994) Extreme Value Theory and Applications , pp. 123-138
    • Pickands, J.1
  • 29
    • 0002433744 scopus 로고    scopus 로고
    • Extreme value statistics and wind storm losses: A case study
    • Rootzén, H. and Tajvidi, N., "Extreme value statistics and wind storm losses: a case study," J. Scand. Actuar. 1, 70-94, (1997).
    • (1997) J. Scand. Actuar. , vol.1 , pp. 70-94
    • Rootzén, H.1    Tajvidi, N.2
  • 30
    • 3342901573 scopus 로고
    • Approximations in extreme value theory
    • Department of Statistics, University of North Carolina, Chapel Hill
    • Smith, R.L., "Approximations in extreme value theory," Tech. Rep. 205, Department of Statistics, University of North Carolina, Chapel Hill, 1987.
    • (1987) Tech. Rep. , vol.205
    • Smith, R.L.1
  • 31
    • 84972496066 scopus 로고
    • Extreme value analysis of environmental time series: An example based on ozone data (with discussion)
    • Smith, R.L., "Extreme value analysis of environmental time series: an example based on ozone data (with discussion)," Stat. Sci. 4, 367-393, (1989).
    • (1989) Stat. Sci. , vol.4 , pp. 367-393
    • Smith, R.L.1
  • 32
    • 0012950799 scopus 로고    scopus 로고
    • Bayesian and frequentist approaches to parametric predictive inference (with discussion)
    • (J.M. Bemardo, J.O. Berger, A.P. Dawid, and A.P.M. Smith, eds), Oxford University Press, Oxford
    • Smith, R.L., "Bayesian and frequentist approaches to parametric predictive inference (with discussion)," in Bayesian Statistics 6 (J.M. Bemardo, J.O. Berger, A.P. Dawid, and A.P.M. Smith, eds), Oxford University Press, Oxford, 589-612, 1999.
    • (1999) Bayesian Statistics , vol.6 , pp. 589-612
    • Smith, R.L.1
  • 34
    • 0023532708 scopus 로고
    • A comparison of maximum likelihood and Bayesian estimators for the three parameter Weilbull distribution
    • Smith, R.L. and Naylor, J.C., "A comparison of maximum likelihood and Bayesian estimators for the three parameter Weilbull distribution," Appl. Stat. 36, 358-369, (1987).
    • (1987) Appl. Stat. , vol.36 , pp. 358-369
    • Smith, R.L.1    Naylor, J.C.2
  • 35
    • 0001900970 scopus 로고
    • Estimating probabilities of extreme sea-levels
    • Tawn, J.A., "Estimating probabilities of extreme sea-levels," Appl. Srat. 41, 77-93, (1992).
    • (1992) Appl. Srat. , vol.41 , pp. 77-93
    • Tawn, J.A.1
  • 36
    • 26444584067 scopus 로고
    • Two test statistics for choice of univariate extreme models
    • (J. Tiago de Oloveira, ed), Reidel, Dordrecht
    • Tiago de Oliveira, J., and Gomes, M.I., "Two test statistics for choice of univariate extreme models," in Statistical Extremes and Applications (J. Tiago de Oloveira, ed), Reidel, Dordrecht, 651-668, 1984.
    • (1984) Statistical Extremes and Applications , pp. 651-668
    • De Tiago Oliveira, J.1    Gomes, M.I.2
  • 37
    • 26444583090 scopus 로고
    • An asymmetric test on the type of distribution of extremes
    • Medelelugen Landbbouwhoge-School Wageningen
    • van Montfort, M.A.J., "An asymmetric test on the type of distribution of extremes," Tech. Rep. 73-18, Medelelugen Landbbouwhoge-School Wageningen, 1973.
    • (1973) Tech. Rep. , vol.73 , Issue.18
    • Van Montfort, M.A.J.1
  • 38
    • 26444483060 scopus 로고
    • On testing a shape parameter in the presence of a scale parameter
    • van Montfort, M.A.J. and Otten, A., "On testing a shape parameter in the presence of a scale parameter," Math. Oper.Forsch. Stat., Ser. Stat. 9, 91-104, (1978).
    • (1978) Math. Oper.Forsch. Stat., Ser. Stat. , vol.9 , pp. 91-104
    • Van Montfort, M.A.J.1    Otten, A.2
  • 39
    • 0034364928 scopus 로고    scopus 로고
    • Modelling extreme wind speeds in regions prone to hurricanes
    • Walshaw, D., "Modelling extreme wind speeds in regions prone to hurricanes," Appl. Stat. 49, 51-62, (2000).
    • (2000) Appl. Stat. , vol.49 , pp. 51-62
    • Walshaw, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.