, Volume 33, Issue 1, pp 165–177 | Cite as

Moment (in-)equalities for differences of order statistics with different sample sizes

  • D. Landers
  • L. Rogge


Leto j:n be thej-th order statistic andq α:n the α-quantile of sample sizen. Ther-th moment of |oj1:n1-oj2:n2| is calculated in terms of hypergeometric distributions. This equality is applied to obtain moment (in-)equalities for |qα:n1-qα:n2|.


Stochastic Process Probability Theory Economic Theory Order Statistic Hypergeometric Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bahadur RR (1966) A note on quantiles in large samples. Ann Math Stat 37:577–580Google Scholar
  2. Bickel PJ (1967) Some contributions to the theory of order statistics. Proc Fifth Berkeley Symp Math Statist Prob 1. Univ of California Press, pp 575–591Google Scholar
  3. Billingsley P (1968) Convergence of probability measures. Wiley, New YorkGoogle Scholar
  4. Blom G (1958) Statistical estimates and transformed beta-variables. Wiley, New YorkGoogle Scholar
  5. Csörgö M, Révész (1978) Strong approximation of the quantile process. Ann Stat 6:882–894Google Scholar
  6. Hoeffding W (1963) Probability inequalities for sums of bounded random variables. J Amer Statist Assoc 58:13–30Google Scholar
  7. Petrov VV (1975) Sums of independent random variables. Springer, New YorkGoogle Scholar
  8. Sen KS (1972) On the Bahadur representation of sample quantiles for sequences of Φ-mixing random variables. J Multivariate Analysis 2:77–95Google Scholar
  9. Wellner JA (1977) A law of the iterated logarithm for functions of order statistics. Ann Stat 5:481–494Google Scholar
  10. van Zwet WR (1964) Convex transformations of random variables. Mathematical Centre Tract 7, Mathematisch Centrum, AmsterdamGoogle Scholar

Copyright information

© Physica-Verlag 1986

Authors and Affiliations

  • D. Landers
    • 1
  • L. Rogge
    • 2
  1. 1.Mathematisches Institut an der UniversitätKöln 41FRG
  2. 2.Universität Duisburg—Gesamthochschule, FB 11— MathematikDuisburg 1FRG

Personalised recommendations