Skip to main content
SpringerLink
Log in

Characterizations of Probability Distributions by Properties of Order Statistics I

  • Conference paper
A Modern Course on Statistical Distributions in Scientific Work

Part of the book series: NATO Advanced Study Institutes Series ((ASIC,volume 17))

Summary

The present paper is the first one attempting to unify and somewhat to extend the theory of characterizing probability distributions by properties of order statistics. Here we discuss the major directions of characterizations for univariate continuous distributions, though the section on characterizing distributions by sequences of moments of order statistics does not make any continuity requirement. In addition, several new results are obtained and many of the proofs of known results are new. The paper is mathematical in nature.

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 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
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. and Rahman, M. (1972). J. Appl. Probability 9, 457–461.

    Article  MathSciNet  MATH  Google Scholar 

  2. Arnold, B. C. (1971/72). Two characterizations of the exponential distribution using order statistics. Unpublished manuscript.

    Google Scholar 

  3. Chan, L. K. (1967). Amer. Math. Monthly 74, 950–951.

    Article  MathSciNet  MATH  Google Scholar 

  4. Crawford, G. B. (1966). Ann. Math. Statist. 37, 1790–1795.

    Article  MathSciNet  MATH  Google Scholar 

  5. Csorgö, M. and Seshadri, V. (1971). Zeitschrift Wahrscheinlichkeitstheorie. verw. Geb. 18, 333–339.

    Article  Google Scholar 

  6. David, H. A. (1970). Order Statistics. Wiley, New York.

    MATH  Google Scholar 

  7. Desu, M. M. (1971). Ann. Math. Statist. 42, 837–838.

    Article  MATH  Google Scholar 

  8. Dubey, S. D. (1966). Indust. Math. 16, 1–22.

    MathSciNet  Google Scholar 

  9. Fisz, M. (1958). Skand. Aktuarietidskr. 1–2, 65–67.

    MathSciNet  Google Scholar 

  10. Galambos, J. (1972). J. Appl. Probability 9, 224–230.

    Article  MathSciNet  MATH  Google Scholar 

  11. Galambos, J. (1974a). Characterizations in terms of properties of the smaller of two observations, to appear.

    Google Scholar 

  12. Galambos, J. (1974b). Characterizations of probability distributions by properties of order statistics - II. In Statistical Distributions in Scientific Work, Vol. 3 Characterizations and Applications. G. P. Patil, S. Kotz and J. K. Ord (ed.). Reidel, Dordrecht and Boston.

    Google Scholar 

  13. Govindarajulu, Z. (1966). Ann. Math. Statist. 37, 1011–1015.

    Article  MathSciNet  MATH  Google Scholar 

  14. Huang, J. S. (1973). Ann. Inst. Statist. Math. ( Tokyo).

    Google Scholar 

  15. Huang, J. S. (1974a). J. Appl. Probability 11, 605–608.

    Article  MathSciNet  MATH  Google Scholar 

  16. Huang, J. S. (1974b). J. Appl. Probability 11, 216–218.

    Article  MathSciNet  MATH  Google Scholar 

  17. Johnson, N. L. and Kotz, S. (1968/70/72). Distributions in Statistics, Vol. I.–IV. Wiley, New York.

    Google Scholar 

  18. Kagan, A. M.; Linnik, Yu. V. and Rao, C. R. (1972). Characterization Problems in Mathematical Statistics (in Russian). Nauka, Moscow (its English translation with an addendum published by Wiley, New York, 1973 ).

    Google Scholar 

  19. Kemperman, J.H.B. (1971). Sankhyā, Ser A 33, 271–288

    Google Scholar 

  20. Klebanov, L. B. (1973). Math. Zametki 13, 121–124.

    MathSciNet  MATH  Google Scholar 

  21. Kotz, S. (1974). International Statist. Review 42, 39 - 65.

    MathSciNet  Google Scholar 

  22. Konheim, A. G. (1971). Amer. Math. Monthly 78, 524.

    Article  MathSciNet  MATH  Google Scholar 

  23. Lukacs, E. and Laha, R. G. (1964). Applications of characteristic functions. Charles Griffin, London.

    MATH  Google Scholar 

  24. Marsaglia, G. (1961). Ann. Math. Statist. 32, 899–900.

    Article  MathSciNet  MATH  Google Scholar 

  25. Patil, G.P. and Seshadri, V. (1964). J. Royal Statist. Soc., Ser B 26, 286–292.

    Google Scholar 

  26. Patil, G. P.; Boswell, M. T.; Ratnaparkhi, M. V. and Kotz, S. (1972/74). Annotated Bibliography of Characterizations of Statistical Distributions (with addendum). To appear.

    Google Scholar 

  27. Pollak, M. (1973). Ann. Statist. 1, 180–182.

    Article  MathSciNet  MATH  Google Scholar 

  28. Puri, P. S. and Rubin, H. (1970). Ann. Math. Statist. 41, 2113–2122.

    Article  MathSciNet  MATH  Google Scholar 

  29. Rossberg, H.-J. (1966). Monatsber. Deutsche Akad. Wiss. Berlin 8, 561–572.

    MathSciNet  MATH  Google Scholar 

  30. Rossberg, H.-J. (1972a). Math. Operationsforsch. u. Statist. 3, 207–216.

    Article  MathSciNet  Google Scholar 

  31. Rossberg, H.-J. (1972b). Sankhyā, Ser A 34, 111–120.

    Google Scholar 

  32. Seshadri, V,: Csörgö, M. and Stephens, M.A. (1969). J. Royal Statist. Soc., Ser B 31, 499–509.

    Google Scholar 

  33. Seshadri, V. and Shuster, J. (1971). A characterization of the uniform distribution and an application to goodness of fit testing. To be published.

    Google Scholar 

  34. Sethurman, J. (1965). Sankhyā, Ser. A 27, 357–264.

    Google Scholar 

  35. Srivastava, R. C. and Wang, Y. H. (1972). Abstract. Bull. Inst. Math. Statist. 1, 192.

    Google Scholar 

  36. Sukhatme, P. V. (1937). Ann. of Eugenics 8, 52–56.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Temple University, Philadelphia, Pa., USA

    J. Galambos

Authors
  1. J. Galambos
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. The Pennsylvania State University, University Park, Pa., USA

    Ganapati P. Patil

  2. Temple University, Philadelphia, Pa., USA

    Samuel Kotz

  3. University of Warwick, Coventry, England

    J. K. Ord

Rights and permissions

Reprints and permissions

Copyright information

© 1975 D. Reidel Publishing Company, Dordrecht-Holland

About this paper

Cite this paper

Galambos, J. (1975). Characterizations of Probability Distributions by Properties of Order Statistics I. In: Patil, G.P., Kotz, S., Ord, J.K. (eds) A Modern Course on Statistical Distributions in Scientific Work. NATO Advanced Study Institutes Series, vol 17. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1848-7_5

Download citation

  • DOI: https://doi.org/10.1007/978-94-010-1848-7_5

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-1850-0

  • Online ISBN: 978-94-010-1848-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation