Relative Frequency of Order Statistics in Independent and Identically Distributed Random Vectors

- Journal title : Communications for Statistical Applications and Methods
- Volume 13, Issue 2, 2006, pp.243-254
- Publisher : The Korean Statistical Society
- DOI : 10.5351/CKSS.2006.13.2.243

Title & Authors

Relative Frequency of Order Statistics in Independent and Identically Distributed Random Vectors

Park, So-Ryoung; Kwon, Hyoung-Moon; Kim, Sun-Yong; Song, Iick-Ho;

Park, So-Ryoung; Kwon, Hyoung-Moon; Kim, Sun-Yong; Song, Iick-Ho;

Abstract

The relative frequency of order statistics is investigated for independent and identically distributed (i.i.d.) random variables. Specifically, it is shown that the probability is no less than the probability at any point when r~~ denotes the r-th order statistic of an i.i.d. discrete random vector and depends on the population probability distribution. A similar result for i.i.d. continuous random vectors is also presented.~~

Keywords

Order statistic;Probability mass function;Probability density function;Relative frequency;

Language

Korean

Cited by

References

1.

박철훈, 송익호, 남동경 (2004), 확률과정, 생능출판사, 서울

2.

Bae, J. and Song, I. (1997). Rank-based detection of weak random signals in a multiplicative noise model. Signal Processing, Vol. 63, 121-131

3.

Balakrishnan, N. and Cohen, A.C. (1991). Order Statistics and Inference, Academic, New York

4.

Blum, R.S. (1996). Locally optimum distributed detection of correlated random signals based on ranks. IEEE Transactions on Information Theory, Vol. 42, 931-942

5.

Brown, C.L. and Zoubir, A.M. (2000). A nonparametric approach to signal detection in impulsive interference. IEEE Transactions on Signal Processing, Vol. 48, 2665-2669

6.

David, H.A. and Nagaraj a, H.N. (2003). Order Statistics (Srd edn), John Wiley and Sons, New York

7.

Hajek, J., Sidak, Z. and Sen, P.K. (1999). Theory of Rank Tests (Znd edn) , Academic, New York

8.

Kassam, S.A. (1988). Signal Detection in Non-Gaussian Noise, Springer-Verlag, New York

9.

Kim, H.G., Song, I., Yoon, S. and Park, S.R. (2002). Nonparametric PN code acquisition using the signed-rank statistic for DS/CDMA systems m frequency-selective Rician fading channels. IEEE Transactions on Vehicular Technology, Vol. 51, 1138-1144

10.

Kim, B.S., Bae, J., Song, I., Kim, S.Y. and Kwon, H. (2006). A comparative analysis of optimum and suboptimum rake receivers in impulsive environment. IEEE Transactions on Vehicular Technology, Vol. 55, (to be published)

11.

Maras, A.M. (2003). Adaptive nonparametric locally optimum Bayes detection in additive non-Gaussian noise. IEEE Transactions on Information Theory, Vol. 49, 204-220

12.

Oppermann, I., Hamalainen, M. and Iinatti, J. (2004). UWB: Theory and Application, John Wiley and Sons, New York

13.

Poor, H.V. and Thomas, J.B, (1993). Advances in Statistical Signal Processing: Vol. 2. Signal Detection, JAI Press, Greenwich