Exact bounds for the expectations of order statistics from non-negative populations

Annals of the Institute of Statistical Mathematics

Volumn 49, Issue 4, 1997, Pages 727-736

  Papadatos, Nickos ^a,b  

^a UNIVERSITY OF ATHENS   (Greece)

^b UNIVERSITY OF CYPRUS   (Cyprus)

Author keywords

Exact bounds; Expectations; Non negative populations; Order statistics

Indexed keywords

EID: 1842473440     PISSN: 00203157     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1003222527882     Document Type: Article

References (10)

1. Arnold, B. C. and Balakrishnan, N. (1989). Relations, bounds and approximations for order statistics, Lecture Notes in Statist., 53, Springer, New York.
2. Balakrishnan, N. (1990). Improving the Hartley-David-Gumbel bound for the mean of extreme order statistics, Statist. Probab. Lett., 9, 291-294.
3. Balakrishnan, N. (1993). A simple application of the binomial-negative binomial relationship in the derivation of sharp bounds for moments of order statistics based on greatest convex minorants, Statist. Probab. Lett., 18, 301-305.
4. Balakrishnan, N. and Bendre, S. M. (1993). Improved bounds for expectations of linear functions of order statistics, Statistics, 24, 161-165.
5. David, H. A. (1981). Order Statistics, 2nd ed., Wiley, New York.
6. Gumbel, E. J. (1954). The maxima of the mean largest value and of the range, Ann. Math. Statist., 25, 76-84.
7. Hartley, H. O. and David, H. A. (1954). Universal bounds for mean range and extreme observations, Ann. Math. Statist., 25, 85-99.
8. Ludwig, O. (1960). Über Erwartungswerte und Varianzen von Ranggrossen in Klein Stichproben, Metrika, 3, 218-233.
9. Moriguti, S. (1953). A modification of Schwarz's inequality with applications to distributions, Ann. Math. Statist., 24, 107-113.
10. Papadatos, N. (1995). Maximum variance of order statistics, Ann. Inst. Statist. Math., 47, 185-193.