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INEQUALITIES FOR CORRELATED BIVARIATE NORMAL DISTRIBUTION FUNCTION

Published online by Cambridge University Press:  18 December 2012

Davaadorjin Monhor
Davaadorjin Monhor*
Affiliation:
Faculty of Geoinformatics, University of West Hungary, Pirosalma u. 1-3, H-8000 Székesfehérvár, Hungary E-mail: [email protected]
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Abstract

We establish several such new inequalities that improve the accuracy of bounding the probability content of bivariate normal distribution function by the Slepian's inequalities. Apart from the improvement of the accuracy, their easy–to–compute form is another attractive feature of these new inequalities which fact is of considerable interest for both theoretical and practical applications. A novel application possibility is mentioned, too.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 27 , Issue 1 , January 2013 , pp. 115 - 123
Copyright
Copyright © Cambridge University Press 2013

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References

1.Agterberg, F.P. (1974). Geomathematics: mathematical background and geoscience applications. Amsterdam: Elsevier Scientific Publishing.Google Scholar
2.Anderson, D.N. & Taylor, S.R. (2002). Application of regularized discrimination analysis to seismic event identification. Bulletin of the Seismological Society of America 92: 2391–2399.CrossRefGoogle Scholar
3.Berge, P.O. (1937). A note on a form of Tchebycheff's theorem for two variables. Biometrika 29: 405–406.Google Scholar
4.Bienaymé, I.J. (1853). Considérations à l'appui de la découverte de Laplace sur loi de probabilité dans la méthode des moindres carrés. Comptes Rendus de l'Academie des Sciences, Paris 37: 309–324.Google Scholar
5.Chebyshev, P.L. (1867). Des Valeurs Moyennes. Journal de Mathématique Pures et Appliquées 12: 177–184.Google Scholar
6.Chebyshev, P.L. in Smith, D.E. (1929). A source book in mathematics. New York: McGraw-Hill, pp. 580–587.Google Scholar
7.Doornbos, R. (1976). Slippage tests. Amsterdam: Mathematical Centre Tracts 15.Google Scholar
8.Frank, H. (1969). Shortest paths in probabilistic graphs. Operations Research 17: 583–599.CrossRefGoogle Scholar
9.Fu, L. & Rilett, L.R. (1998). Expected shortest paths in dynamic and stochastic traffic networks. Transportation Research B 32: 499–516.CrossRefGoogle Scholar
10.Gauss, C.F. (1823). Theoria Combinationis Observationum Erroribus minimis Obnoxiae, Pars Prior, Pars Posterior, Supplementum. Göttingen, 1923.Google Scholar
11.Gauss, K.F. (1995). Theory of the Combination of Observations least Subject to Errors, Part One, Part Two, Supplement. Translated by Stewart, G. W., Philadelphia, 1995.CrossRefGoogle Scholar
12.Geske, R. (1979a). A note on an analytical valuation formula for unprotected American call options on stocks with known dividends. Journal of Financial Economics 4: 375–380.CrossRefGoogle Scholar
13.Geske, R. (1979b). The valuation of compound options. Journal of Financial Economics 7: 63–82.CrossRefGoogle Scholar
14.Hassibi, A. & Boyd, S. (1998). Integer Parameter Estimation in Linear Models with Applications to GPS. IEEE Transactions on Signal Processng 46: 2938–2952.CrossRefGoogle Scholar
15.Hutchinson, T.P. & Lai, C.D. (1990). Continuous bivariate distributions: Emphasizing applications. Adelaide: Rumsby.Google Scholar
16.Jeng, F.C. & Woods, J.W. (1990). Simmulated Annealing compound Gauss-Markov random fields. IEEE Transactions on Information Theory 36: 94–107.CrossRefGoogle Scholar
17.Keppo, J. (2005). Pricing of point-to-point bandwidth contracts. Mathematical Methods of Operations Research 61: 191–198.CrossRefGoogle Scholar
18.Lal, D.N. (1955). A note on a form of Tchebycheff's inequality for two variables. Sankhya 15: 317–320.Google Scholar
19.Lui, P. (1983). Optimal paths in graphs with stochastic or multidimensional weights. Communications of the Association for Computing Machinery 26: 670–676.CrossRefGoogle Scholar
20.Monhor, D. (2007). An Chebyshev inequality for multivariate normal distibution. Probability in the Engineering and Informational Sciences 21: 289–300.CrossRefGoogle Scholar
21.Olkin, I. & Pratt, J.W. (1958). A multivariate Tchebysheff's inequality. Annals of Mathematical Statistics 29: 226–234.CrossRefGoogle Scholar
22.Plackett, R. L. (1954). A reduction formula for normal multivariate integrals. Biometrika 41: 351–360.CrossRefGoogle Scholar
23.Pólya, G. (1949). Remarks on computing the probability integral in one and two dimensions. Proceedings of the Berkeley Symposium on Mathematical Statistics and Probability, Statistics Laboratory, Department of Mathematics, University of California, August 13–18, 1945, January 27–29, 1946, Edited by Jerzy Neyman, Berkeley, CA: University of California Press, pp. 63–79.Google Scholar
24.Ross, S.M. (2007). Introduction to probability models. 10th, New York: Academic Press, Elsevier.Google Scholar
25.Sheppard, W.F. (1900). On the calculation of the double integral expressing normal correlation. Transactions of the Cambridge Philosophical Society 19, 23–66.Google Scholar
26.Slepian, D. (1962). The one-sided barrier problem for Gaussian noise. Bell System Technical Journal 41: 463–501.CrossRefGoogle Scholar
27.Stulz, R. M. (1982). Options on the minimum or the maximum of two risky assets: analysis and applications. Journal of Financial Economics 10: 161–185.CrossRefGoogle Scholar
28.Williams, J. D. (1946). An approximation to the probability integral. Annals of Mathematical Statistics 17: 363–365.CrossRefGoogle Scholar
29.Wozencraft, J.M. & Jacobs, I.M. (1965). Principles of Communications Engineering. New York and London: John Wiley.Google Scholar
30.Zhang, P.G. (1995). Correlation digital options. The journal of financial engineering 4: 75–96.Google Scholar