Kullback-Leibler Information in View of an Extended Version of κ-Records

- Journal title : Communications for Statistical Applications and Methods
- Volume 20, Issue 1, 2013, pp.1-13
- Publisher : The Korean Statistical Society
- DOI : 10.5351/CSAM.2013.20.1.001

Title & Authors

Kullback-Leibler Information in View of an Extended Version of κ-Records

Ahmadi, Mosayeba; Mohtashami Borzadaran, G.R.;

Ahmadi, Mosayeba; Mohtashami Borzadaran, G.R.;

Abstract

This paper introduces an extended version of -records. Kullback-Leibler (K-L) information between two generalized distributions arising from -records is derived; subsequently, it is shown that K-L information does not depend on the baseline distribution. The behavior of K-L information for order statistics and -records, is studied. The exact expressions for K-L information between distributions of order statistics and upper (lower) -records are obtained and some special cases are provided.

Keywords

Order statistics;-records;Kullback-Leibler information;

Language

English

Cited by

1.

References

1.

Ahmadi, J. and Arghami, N. R. (2001). Some univariate stochastic orders on record values, Communication Statistics Theory and Methods, 30, 69-74.

2.

Ahmadi, J. and Balakrishnan, N. (2012). Outer and inner prediction intervals for order statistics intervals based on current records, Statistical Papers, 53, 789-802.

3.

Ahmadi, J., MirMostafaee, S. M. T. K. and Balakrishnan, N. (2010). Nonparametric prediction intervals for future record intervals based on order statistics, Statistics and Probability Letters, 80, 1663-1672.

4.

Arnold, B. C., Balakrishnan, N. and Nagaraja, H. N. (1998). Records, Wiley, New York.

5.

Arnold, B. C., Balakrishnan, N. and Nagaraja, H. N. (2008). A First Course in Order Statistics (Classic Edition), SIAM, Philadelphia.

6.

Balakrishnan, N., Kamps, U. and Kateri, M. (2009). Minimal repair under a step stress test, Statistics and Probability Letters, 79, 1548-1558.

7.

Bartoszewicz, J. (2009). On a representation of weighted distributions, Statistics and Probability Letters, 79, 1690-1694.

8.

Cover, T. M. and Thomas, J. A. (2006). Elements of Information Theory, John Wiley and Sons, Inc.

9.

Csiszar, I. (1963). Eine informationstheoretische Ungleichung und ihre Anwendung auf den Beweis der Ergodizitat von Markoffschen Ketten. Publication of the Mathematical Institute of Mathematics, Hungarian Academy of Sciences, 8, 85-108.

10.

David, H. A. and Nagaraja, H. N. (2003). Order Statistics, Third ed., Wiley, Hoboken, NJ.

11.

Ebrahimi, N., Soofi, E. S. and Zahedi, H. (2004). Information properties of order statistics and spacings, IEEE Transactions on Information Theory, 50, 177-183.

12.

Fisher, R. A. (1934). The effect of methods of ascertainment upon the estimation of frequencies, Annals of Eugenics, 6, 13-25.

13.

Gupta, R. C. (1984). Relationship between order statistics and record values and some characterization result, Journal of Applied Probability, 21, 425-430.

14.

Gupta, R. C. and Ahsanullah, M. (2004). Some characterization results based on the conditional expectation of a function of non-adjacent order statistic (record value), Annals of the Institute of Statistical Mathematics, 56, 721-732.

15.

Gupta, R. C. and Keating, J. P. (1986). Relations for the reliability measures under length biased sampling, Scandinavian Journal of Statistics, 13, 49-56.

16.

Jones, M. C. (2004). Families of distributions arising from distributions of order statistics (with discussion), Test, 13, 1-43.

17.

Kullback, S. and Leibler, R. A. (1951). On information and sufficiency, Annals of Mathematical Statistics, 22, 79-86.

18.

MirMostafaee, S. T. K. and Ahmadi, J. (2012). General families of distributions arising from distributions of record statistics, Submited.

19.

Nevzorov, V. B. (2000). On a limit relation between order statistics and records, Journal of Mathe-matical Sciences, 99, 1149-1153.

20.

Patil, G. P. and Rao, C. R. (1977). Weighted distributions: A survey of their application. In P. R. Krishnaiah (Ed.), Applications of Statistics, (pp. 383-405). North Holland Publishing Company.

21.

Patil, G. P. and Rao, C. R. (1978). Weighted distributions and size-biased sampling with applications to wildlife populations and human families, Biometrics, 34, 179-180.

22.

Rao, C. R. (1965). Weighted distributions arising out of methods of ascertainment. In Classical and Contagious Discrete Distributions, G. P. Patil (Eds). Calcutta: Pergamon Press and Statistical Publishing Society, 320-332.

23.

Rao, C. R. (1985). Weighted distributions arising out of methods of ascertainment: What population does a sample represent. In the Celebration of Statistics, A. C. Atkinson and S. E. Fienberg eds. Springer Verlag, New York, Chapter 24, 543-569.

24.

Shaked, M. and Shanthikumar, J. G. (1994). Stochastic Orders and Their Applications, Academic Press, New York.

25.

Shannon, C. E. (1948). A mathematical theory of communication, Bell System Technical Journal, 27, 379-423 and 623-656.

26.

Wilks, S. S. (1948). Order statistics, Bulletin of the American Mathematical Society, 54, 6-50.