Skip to main content
Log in

Moments of order statistics of Topp–Leone distribution

  • Published:
Statistical Papers Aims and scope Submit manuscript

Abstract

We derive explicit algebraic expressions for both of the single and product moments of order statistics from Topp–Leone distribution. We also give an identity about single moments of order statistics. These expressions will be useful for computational purposes.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Arnold BC, Balakrishnan N, Nagaraja HN (1992) A first course in order statistics. Wiley, New York

    MATH  Google Scholar 

  • Balakrishnan N, Malik HJ, Malik SE (1988) Recurrence relations and identities for moments of order statistics-II: specific continuous distributions. Commun Stat Theory Methods 17: 2657–2694

    Article  MathSciNet  MATH  Google Scholar 

  • Ghitany ME (2007) Asymptotic distribution of order statistics from the Topp–Leone distribution. Int J Appl Math 20: 371–376

    MathSciNet  MATH  Google Scholar 

  • Ghitany ME, Kotz S, Xie M (2005) On some reliability measures and their stochastic orderings for the Topp–Leone distribution. J Appl Stat 32: 715–722

    Article  MathSciNet  MATH  Google Scholar 

  • Kotz S, Nadarajah S (2006) J-shaped distribution, Topp and Leone’s. Encyclopedia of statistical sciences, vol 6, 2nd edn. Wiley, New York, p 3786

    Google Scholar 

  • Kotz S, Van Dorp JR (2004) Beyond beta—other continuous families of distributions with bounded support and applications. World Scientific, Singapore

    Book  MATH  Google Scholar 

  • Nadarajah S (2008) Explicit expressions for moments of order statistics. Stat Probab Lett 78: 196–205

    Article  MathSciNet  MATH  Google Scholar 

  • Nadarajah S, Kotz S (2003) Moments of some J-shaped distributions. J Appl Stat 30: 311–317

    MathSciNet  MATH  Google Scholar 

  • Raqab MZ (2004) Generalized exponential distribution: moments of order statistics. Statistics 38: 29–41

    Article  MathSciNet  MATH  Google Scholar 

  • Thomas PY, Samuel P (2008) Recurrence relations for the moments of order statistics from a beta distribution. Stat Pap 49: 139–146

    Article  MathSciNet  MATH  Google Scholar 

  • Topp CW, Leone FC (1955) A family of J-shaped frequency functions. J Am Stat Assoc 50: 209–219

    Article  MathSciNet  MATH  Google Scholar 

  • Van Dorp JR, Kotz S (2004) Modeling income distributions using elevated distributions on a bounded domain. Unpublished manuscript, The George Washington University, Washington DC

  • Vicari D, Van Dorp JR, Kotz S (2008) Two-sided generalized Topp and Leone (TS-GTL) distributions. J Appl Stat 35: 1115–1129

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ali İ. Genç.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Genç, A.İ. Moments of order statistics of Topp–Leone distribution. Stat Papers 53, 117–131 (2012). https://doi.org/10.1007/s00362-010-0320-y

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00362-010-0320-y

Keywords

Mathematics Subject Classification (2000)

Navigation