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Selfdecomposable distributions for maxima of independent random vectors
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  • Published: June 1990

Selfdecomposable distributions for maxima of independent random vectors

  • E. I. Pancheva1 

Probability Theory and Related Fields volume 84, pages 267–278 (1990)Cite this article

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Summary

In the present paper the limit laws for conveniently normalized multivariate sample extremes are characterized by means of the decomposability of probability distributions. Continuous automorphisms ofR d =[−∞,∞]d with respect to the operation “v” defined by x Λ y=(max(x i, yi),i=1... d) are treated as norming mappings. An integral representation of the limit distributions is found using their log-concavity and a decomposition ofR d in orbits of the norming family. Finally an example is given as an illustration.

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References

  1. Aczel, J.: Some general methods in the theory of functional equations with one variable. New applications of functional equations (in Russian). Uspehi Mathem. Nauk3 (69), 3–67 (1956)

    Google Scholar 

  2. Balkema, A.A., Resnick, S.I.: Max-infinite divisibility. J. Appl. Probab.14, 309–319 (1977)

    Google Scholar 

  3. Galambos, J.: The asymptotic theory for extreme order statistics. New York: Wiley 1978 (Russian translation Nauka, Moskow 1984)

    Google Scholar 

  4. de Haan, L., Resnick, S.I.: Limit theory for multivariate sample extremes. Z. Wahrscheinlichkeitstheor. Verw. Geb.40, 317–337 (1977)

    Google Scholar 

  5. Pancheva, E.: Limit theorems for extreme order statistics under nonlinear normalization (Lect. Notes Math., vol. 1155, pp. 284–309). Berlin Heidelberg New York: Springer 1984

    Google Scholar 

  6. Pancheva, E.: General limit theorems for maxima of independent random variables (in Russian). Probab. Theor. Appl.4, 31, 730–744 (1986)

    Google Scholar 

  7. Sharp, M.: Operator-stable probability distributions on vector groups. Trans. Am. Math. Soc.136, 51–65 (1969)

    Google Scholar 

  8. Urbanik, K.: Levy's probability measures on Euclidean spaces. Studia Mathem. XLIV, 119–148 (1972)

    Google Scholar 

  9. Zolotarev, V.M.: Two analytic problems in the probability theory (in Russian). Abstracts from XX School-Colloquium on probability theory and Mathem. Statist., Bakuriani 1986, USSR

  10. Phelps, R.: Lectures on Choquet's theorem. New Jersey: Princeton 1966

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Bulgarian Academy of Sciences, 1113, Sofia, Bulgaria

    E. I. Pancheva

Authors
  1. E. I. Pancheva
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Additional information

Research supported in part by the Committee of Science, Bulgarian Concil of Ministers, under contract no. 60/1987

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Cite this article

Pancheva, E.I. Selfdecomposable distributions for maxima of independent random vectors. Probab. Th. Rel. Fields 84, 267–278 (1990). https://doi.org/10.1007/BF01197848

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  • Received: 08 February 1988

  • Revised: 13 June 1989

  • Issue Date: June 1990

  • DOI: https://doi.org/10.1007/BF01197848

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Keywords

  • Probability Distribution
  • Stochastic Process
  • Probability Theory
  • Integral Representation
  • Random Vector
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