Sharp bounds for expectations of kth record increments

Australian and New Zealand Journal of Statistics

Volumn 46, Issue 4, 2004, Pages 665-673

  Danielas, Katarzyna ^a,c   Raqab, Mohammad Z ^b  

^a POLISH ACADEMY OF SCIENCES   (Poland)

^b UNIVERSITY OF JORDAN   (Jordan)

^c INSTITUTE OF MATHEMATICS   (Poland)

Author keywords

Holder's inequality; Kth record; Moriguti's inequality; Sharp bound

Indexed keywords

EID: 4344654779     PISSN: 13691473     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1467-842x.2004.00361.x     Document Type: Article

References (12)

1. ARNOLD, B.C., BALAKRISHNAN, N. & NAGARAJA, H.N. (1998). Records. New York: John Wiley.
2. DANIELAK, K. (2004). Distribution-free bounds for expectations of increments of records. J. Statist. Plann. Inference (to appear).
3. DZIUBDZIELA, W. & KOPOCIŃSKI, B. (1976). Limiting properties of the kth record values. Appl. Math. (Warsaw) 15, 187-190.
4. GAJEK, L. & OKOLEWSKI, A. (2003). Projection bounds on expectations of record statistics from restricted families. J. Statist. Plann. Inference 110, 97-108.
5. GRUDZIEŃ, Z. & SZYNAL, D. (1985). On the expected values of kth record values and associated characterizations of distributions. In Probability and Statistical Decision Theory, Vol. A, eds F. Konecny, J. Mogyoródy, & W. Wertz, pp. 119-127. Dordrecht: Reidel.
6. MORIGUTI, S. (1953). A modification of Schwarz's inequality with applications to distributions. Ann. Math. Statist. 24, 107-113.
7. NAGARAJA, H.N. (1978). On the expected values of record values. Austral. J. Statist. 20, 176-182.
8. RAQAB, M.Z. (1997). Bounds based on greatest convex minorants for moments of record values. Statist. Probab. Lett. 36, 35-41.
9. RAQAB, M.Z. (2004). Projection p-norm bounds on the moments of kth record increments. J. Statist. Plann. Inference 124, 301-315.
10. RAQAB, M.Z. & RYCHLIK, T. (2002). Sharp bounds for the mean of the kth record value. Comm. Statist. Theory Methods 31, 1927-1938.
11. RYCHLIK, T. (1997). Evaluating improvements of records. Appl. Math. (Warsaw) 24, 315-324.
12. RYCHLIK, T. (2001). Projecting Statistical Functional. Lecture Notes in Statistics, 160. New York: Springer-Verlag.