Skip to main content
SpringerLink
Log in

Record Values in Archimedean Copula Processes

  • Chapter
Asymptotic Methods in Probability and Statistics with Applications

Part of the book series: Statistics for Industry and Technology ((SIT))

Abstract

We investigate the asymptotic behavior of record values X(n) for some types of Archimedean copula processes. It is shown that the set of all limit distribution functions for X(n),normed and centered in a suitable way, under some restrictions on parameters of these processes, coincides with the corresponding set of asymptotic distributions of record values in the sequences of i.i.d. random variables.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ahsanullah, M. (1995). Record Statistics, Commack, NY: Nova Science Publishers.

    Google Scholar 

  2. Arnold, B. C., Balakrishnan, N. and Nagaraja, H. N. (1998). Records, New York: John Wiley & Sons.

    Book  MATH  Google Scholar 

  3. Balakrishnan, N. and Nevzorov, V. (1997). Stirling numbers and records, In Advances in Combinatorial Methods and Applications to Probability and Statistics (Ed., N. Balakrishnan), pp. 189–200, Boston: Birkhäuser.

    Chapter  Google Scholar 

  4. Ballerini, R. (1994). A dependent Fα-scheme, Statistics & Probability Letters, 21, 21–25.

    Article  MathSciNet  MATH  Google Scholar 

  5. Ballerini, R. and Resnick, S. (1987). Embedding sequences of successive maxima in extremal processes, with applications, Journal of Applied Probability, 24, 827–837.

    Article  MathSciNet  MATH  Google Scholar 

  6. Deheuvels, P. and Nevzorov, V. B. (1993). Records in the Fα-scheme. I. Martingale properties, Notes of Sci. Semin. POMI, 207, 19–36 (in Russian). English version in: Journal of Mathematical Science,81 (1996), 2368–2378.

    Google Scholar 

  7. Deheuvels, P. and Nevzorov, V. B. (1994). Records in the Fα-scheme. II. Limit laws, Notes of Sci. Semin. POMI,216, 42–51 (in Russian). English version in: Journal of Mathematical Science, 88 (1998), 2368–2378.

    Google Scholar 

  8. Galambos, J. (1978). The Asymptotic Theory of Extreme Order Statistics, New York: John Wiley & Sons.

    MATH  Google Scholar 

  9. Green, R. F. (1976). Partial attraction of maxima, Journal of Applied Probability, 13, 159–163.

    Article  MathSciNet  MATH  Google Scholar 

  10. Nevzorov, V. B. (1984). Record times in the case of nonidentically distributed random variables, Theory of Probability and Its Applications,29, 808–809.

    Google Scholar 

  11. Nevzorov, V. B. (1985). Records and inter-record times for sequences of nonidentically distributed random variables, Notes of Sci. Semin. LOMI, 142, 109–118 (in Russian). English version: in Journal of Soviet Mathematics,36 (1987), 510–516.

    Google Scholar 

  12. Nevzorov, V. B. (1986). Two characterizations using records, In Stability Problems for Stochastic Models (Eds., V. V. Kalashnikov, B. Penkov and V. M. Zolotarev), Lecture Notes in Mathematics 1233, pp. 79–85, Berlin: Springer-Verlag.

    Chapter  Google Scholar 

  13. Nevzorov, V. B. (1995). Asymptotic distributions of records in nonstationary schemes, Journal of Statistical Planning and Inference, 44, 261–273.

    Article  MathSciNet  Google Scholar 

  14. Nevzorov, V. B. and Stepanov, A. V. (1988). Records: Martingale approach to finding of moments, In Rings and Modules. Limit Theorems of Probability Theory (Eds., Z. I. Borevich and V. V. Petrov), 2, 171–181, St.-Petersburg: St.-Petersburg State University.

    Google Scholar 

  15. Nevzorova, L. N., Nevzorov, V. B. and Balakrishnan, N. (1997). Characterizations of distributions by extremes and records in Archimedean copula process, In Advances in the Theory and Practice of Statistics: A Volume in Honor of Samuel Kotz (Eds., N. L. Johnson and N. Balakrishnan), pp. 469–478, New York: John Wiley & Sons.

    Google Scholar 

  16. Pfeifer, D. (1989). Extremal processes, secretary problems and the 1/e law, Journal of Applied Probability, 26, 722–733.

    Article  MathSciNet  MATH  Google Scholar 

  17. Pfeifer, D. (1991). Some remarks on Nevzorov’s record model, Advances in Applied Probability, 23, 823–834.

    Article  MathSciNet  MATH  Google Scholar 

  18. Resnick, S. I. (1973a). Record values and maxima, Annals of Probability, 1, 650–662.

    Article  MathSciNet  MATH  Google Scholar 

  19. Resnick, S. I. (1973b). Limit laws for record values, Stochastic Processes and their Applications, 1, 67–82.

    Article  MathSciNet  MATH  Google Scholar 

  20. Yang, M. C. K. (1975). On the distribution of the inter-record times in an increasing population, Journal of Applied Probability, 12, 148–154.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. McMaster University, Hamilton, Ontario, Canada

    N. Balakrishnan

  2. St. Petersburg Humanitarian University of Trade Unions, St. Petersburg, Russia

    L. N. Nevzorova

  3. St. Petersburg State University, St. Petersburg, Russia

    V. B. Nevzorov

Authors
  1. N. Balakrishnan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. N. Nevzorova
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. B. Nevzorov
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, Ontario, L8S 4K1, Canada

    N. Balakrishnan

  2. Department of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, Russia

    I. A. Ibragimov  & V. B. Nevzorov  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer Science+Business Media New York

About this chapter

Cite this chapter

Balakrishnan, N., Nevzorova, L.N., Nevzorov, V.B. (2001). Record Values in Archimedean Copula Processes. In: Balakrishnan, N., Ibragimov, I.A., Nevzorov, V.B. (eds) Asymptotic Methods in Probability and Statistics with Applications. Statistics for Industry and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0209-7_23

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-0209-7_23

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6663-1

  • Online ISBN: 978-1-4612-0209-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation