Asymptotic Value of the Probability That the First Order Statistic Is from Null Hypothesis

Affiliation(s)

Department of Electrical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, South Korea.

School of Information, Communications, and Electronics Engineering, The Catholic University of Korea, Bucheon, South Korea.

College of Information and Communication Engineering, Sungkyunkwan University, Suwon, South Korea.

Department of Electrical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, South Korea.

School of Information, Communications, and Electronics Engineering, The Catholic University of Korea, Bucheon, South Korea.

College of Information and Communication Engineering, Sungkyunkwan University, Suwon, South Korea.

ABSTRACT

When every element of a random
vector __ X__ =(

Cite this paper

Song, I. , Lee, S. , Park, S. and Yoon, S. (2013) Asymptotic Value of the Probability That the First Order Statistic Is from Null Hypothesis.*Applied Mathematics*, **4**, 1702-1705. doi: 10.4236/am.2013.412231.

Song, I. , Lee, S. , Park, S. and Yoon, S. (2013) Asymptotic Value of the Probability That the First Order Statistic Is from Null Hypothesis.

References

[1] T. Yücek and H. Arslan, “A Survey of Spectrum Sensing Algorithms for Cognitive Radio Applications,” IEEE Communications Surveys and Tutorials, Vol. 11, No. 1, 2009, pp. 116-130.

[2] Z. Quan, S. Cui, A. H. Sayed and H. V. Poor, “Optimal Multiband Joint Detection for Spectrum Sensing in Cognitive Radio Networks,” IEEE Transactions on Signal Processing, Vol. 57, No. 3, 2009, pp. 1128-1140.

http://dx.doi.org/10.1109/TSP.2008.2008540

[3] A. Taherpour, M. Nasiri-Kenari and S. Gazor, “Multiple Antenna Spectrum Sensing in Cognitive Radios,” IEEE Transactions on Wireless Communications, Vol. 9, No. 2, 2010, pp. 814-823.

http://dx.doi.org/10.1109/TWC.2009.02.090385

[4] P. Paysarvi-Hoseini and N. C. Beaulieu, “Optimal Wideband Spectrum Sensing Framework for Cognitive Radio Systems,” IEEE Transactions on Signal Processing, Vol. 59, No. 3, 2011, pp. 1170-1182.

http://dx.doi.org/10.1109/TSP.2010.2096220

[5] T. An, H.-K. Min, S. Lee and I. Song, “Likelihood Ratio Test for Wideband Spectrum Sensing,” Proceedings of IEEE Pacific Rim Conference on Communications, Computers and Signal Processing, Victoria, 27-29 August 2013.

[6] H. A. David and H. N. Nagaraja, “Order Statistics,” 3rd edition, John Wiley and Sons, New York, 2003.

http://dx.doi.org/10.1002/0471722162

[7] I. Song, K. S. Kim, S. R. Park and C. H. Park, “Principles of Random Processes,” Kyobo, Seoul, 2009.

[8] V. K. Rohatgi and A. K. Md. E. Saleh, “An Introduction to Probability and Statistics,” 2nd edition, John Wiley and Sons, New York, 2001.

[9] I. S. Gradshteyn and I. M. Ryzhik, “Table of Integrals, Series, and Products,” Academic, New York, 1980.

[10] J. Hajek, Z. Sidak and P. K. Sen, “Theory of Rank Tests,” 2nd edition, Academic, New York, 1999.

[1] T. Yücek and H. Arslan, “A Survey of Spectrum Sensing Algorithms for Cognitive Radio Applications,” IEEE Communications Surveys and Tutorials, Vol. 11, No. 1, 2009, pp. 116-130.

[2] Z. Quan, S. Cui, A. H. Sayed and H. V. Poor, “Optimal Multiband Joint Detection for Spectrum Sensing in Cognitive Radio Networks,” IEEE Transactions on Signal Processing, Vol. 57, No. 3, 2009, pp. 1128-1140.

http://dx.doi.org/10.1109/TSP.2008.2008540

[3] A. Taherpour, M. Nasiri-Kenari and S. Gazor, “Multiple Antenna Spectrum Sensing in Cognitive Radios,” IEEE Transactions on Wireless Communications, Vol. 9, No. 2, 2010, pp. 814-823.

http://dx.doi.org/10.1109/TWC.2009.02.090385

[4] P. Paysarvi-Hoseini and N. C. Beaulieu, “Optimal Wideband Spectrum Sensing Framework for Cognitive Radio Systems,” IEEE Transactions on Signal Processing, Vol. 59, No. 3, 2011, pp. 1170-1182.

http://dx.doi.org/10.1109/TSP.2010.2096220

[5] T. An, H.-K. Min, S. Lee and I. Song, “Likelihood Ratio Test for Wideband Spectrum Sensing,” Proceedings of IEEE Pacific Rim Conference on Communications, Computers and Signal Processing, Victoria, 27-29 August 2013.

[6] H. A. David and H. N. Nagaraja, “Order Statistics,” 3rd edition, John Wiley and Sons, New York, 2003.

http://dx.doi.org/10.1002/0471722162

[7] I. Song, K. S. Kim, S. R. Park and C. H. Park, “Principles of Random Processes,” Kyobo, Seoul, 2009.

[8] V. K. Rohatgi and A. K. Md. E. Saleh, “An Introduction to Probability and Statistics,” 2nd edition, John Wiley and Sons, New York, 2001.

[9] I. S. Gradshteyn and I. M. Ryzhik, “Table of Integrals, Series, and Products,” Academic, New York, 1980.

[10] J. Hajek, Z. Sidak and P. K. Sen, “Theory of Rank Tests,” 2nd edition, Academic, New York, 1999.