Uniform rates of convergence in extreme-value theory. Normal and gamma models

L. Canto E Castro

Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications (1987)

  • Volume: 90, Issue: 6, page 25-41
  • ISSN: 0246-1501

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Canto E Castro, L.. "Uniform rates of convergence in extreme-value theory. Normal and gamma models." Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications 90.6 (1987): 25-41. <http://eudml.org/doc/80640>.

@article{CantoECastro1987,
author = {Canto E Castro, L.},
journal = {Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications},
keywords = {uniform rates of convergence; extreme-value theory; normal distribution; domain of attraction for maxima of the Gumbel law; uniform upper and lower bounds; gamma distributions},
language = {eng},
number = {6},
pages = {25-41},
publisher = {UER de Sciences exactes et naturelles de l'Université de Clermont},
title = {Uniform rates of convergence in extreme-value theory. Normal and gamma models},
url = {http://eudml.org/doc/80640},
volume = {90},
year = {1987},
}

TY - JOUR
AU - Canto E Castro, L.
TI - Uniform rates of convergence in extreme-value theory. Normal and gamma models
JO - Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications
PY - 1987
PB - UER de Sciences exactes et naturelles de l'Université de Clermont
VL - 90
IS - 6
SP - 25
EP - 41
LA - eng
KW - uniform rates of convergence; extreme-value theory; normal distribution; domain of attraction for maxima of the Gumbel law; uniform upper and lower bounds; gamma distributions
UR - http://eudml.org/doc/80640
ER -

References

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  1. Anderson, C.W. (1971). Contributions to the asymptotic theory of extreme values, Ph. D. Thesis, Imperial College, London. 
  2. Anderson, C.W. (1976). Extreme value theory and its approximations. Proc. Symp. Reliability Technology. Bradford, UKAEA. 
  3. Canto e Castro, L. (1936). Velocidade de convergência em teoria de valores extremes. Tese de Restrado, Fac. Ciências, Lisboa. 
  4. Cohen, J.P. (1982a). The penultimate form of approximation to normal extremes. Adu. Appl. Prob., 14, 324-339. Zbl0486.62026MR650126
  5. Cohen, J.P. (1982b). Convergence rates for the ultimate and penultimate approximations in extreme value theory. Adv. Appl. Prob., 14, 833-854. Zbl0496.62019MR677559
  6. Fisher, R.A. and L.H.C. Tippet (1928). Limiting forms of the large or smallest member of a sample, Proc. Camb. Phil. Soc., 24, 180-190. Zbl54.0560.05JFM54.0560.05
  7. Galambos, J. (1978). The Asymptotic Theory of Extreme Order Statistics, Wiley, New York. Zbl0381.62039MR489334
  8. Gnedenko, B. (1943). Sur la distribution limite du terme maximum d'une série aléatoire, Ann. Math.,44, 423-453. Zbl0063.01643MR8655
  9. Gomes, M.I. (1978). Some probabilistic and statistical problems in extreme value theory, Ph.D. Thesis, Sheffield, England. 
  10. Gomes, M.I. (1984). Penultimate limiting forms in extreme value theory, Ann. Inst. Statist. Math., 36, Part A, 71-85. Zbl0561.62015MR752007
  11. Hall, P. (1979). On the rate of convergence of normal extremes, J. Appl. Prob., 16, 433-439. Zbl0403.60024MR531778
  12. Uzgoren, N.T. (1954). The asymptotic development of the distribution of the extreme values of a sample, Studies in Mathematics and Mechanics Presented to R. von Mises, Academic Press, New York. Zbl0058.35105MR67415

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