ξ1 ve ξ2, tüm momentleri sonlu olan rasgele değişkenler olsunlar. U kümesine ξ1 ve ξ2’nin korelasyonsuzluk kümesi denir. Bu makalede birleşik normal rasgele değişkenlerin mümkün korelasyonsuzluk kümelerinin tarifi verilir.
BENES, V., STEPAN, J. (eds) J. (1997) Distributions With Given Marginals And Moment Problems. Kluwer Academic Publishers.
DALL’AGLIO, G. (1988), Decomposability Of Probability Distributions. Rend. Sem. Math. Fis. Milano, 58, Pp. 239-245.
DALL’AGLIO, G. (1990) Somme Di Variabili Aleatore e Convoluzioni. Scritti in Omagio a Luciano Daboni, Lint, Trieste, pp. 95-100.
DALL'AGLIO, G., KOTZ, S., SALINETTI, G. (eds) (1991) Advances in Probability Distributions with Given Marginals. Kluwer Academic Publishers.
FELLER, W. (1968) An Introduction to Probability Theory and Its Applications. 2-nd Ed. Wiley, New-York.
GADETSKA S., OSTROVSKA S. (2002) Copulas and Uncorrelation Sets. Hacettepe Üniversitesi İstatistik Günleri 2002. Sempozyum Özetleri, p.20.
OSTROVSKA, S. (1998) A Scale of Degrees of Independence of Random Variables. Indian J. of Pure and Applied Math., 29, (5), pp. 461-471.
OSTROVSKA, S. Uncorrelatedness and Correlatedness of Powers of Random Variables. (2002) Archiv der Mathematik, 79. Pp. 141-146.
PAPOULIS, A. (1991) Probability, Random Variables, and Stochastic Processes 3-d Ed. McGRAW-HILL, Inc.
PRICE, R. (1965) A Useful Theorem for Nonlinear Devices Having Gaussian Inputs. IRE, PGIT, Vol. IT-4.
RENYI, A. (1959) On Measures of Dependence. Acta Math. Acad. Sci. Hungar., 10, pp. 441-451.
STOYANOV, J. (1998) Global Dependency Measure for Sers of Random Elements "The Italian Problem" and Some Consequences. In: 1. Karatzas, B. S. Rajput. M.S. Taqqu (eds) Stochastic Processes and Relared Topics. Birkhäuser, pp. 357-375.
Uncorrelation Sets for Jointly Normal Random Variables
Let ξ1, and ξ2 be random variables with finite moments of all orders. The set U is called the uncorrelation set of ξ1 and ξ2. In this paper we describe possible uncorrelation sets of jointly normal random variables.
BENES, V., STEPAN, J. (eds) J. (1997) Distributions With Given Marginals And Moment Problems. Kluwer Academic Publishers.
DALL’AGLIO, G. (1988), Decomposability Of Probability Distributions. Rend. Sem. Math. Fis. Milano, 58, Pp. 239-245.
DALL’AGLIO, G. (1990) Somme Di Variabili Aleatore e Convoluzioni. Scritti in Omagio a Luciano Daboni, Lint, Trieste, pp. 95-100.
DALL'AGLIO, G., KOTZ, S., SALINETTI, G. (eds) (1991) Advances in Probability Distributions with Given Marginals. Kluwer Academic Publishers.
FELLER, W. (1968) An Introduction to Probability Theory and Its Applications. 2-nd Ed. Wiley, New-York.
GADETSKA S., OSTROVSKA S. (2002) Copulas and Uncorrelation Sets. Hacettepe Üniversitesi İstatistik Günleri 2002. Sempozyum Özetleri, p.20.
OSTROVSKA, S. (1998) A Scale of Degrees of Independence of Random Variables. Indian J. of Pure and Applied Math., 29, (5), pp. 461-471.
OSTROVSKA, S. Uncorrelatedness and Correlatedness of Powers of Random Variables. (2002) Archiv der Mathematik, 79. Pp. 141-146.
PAPOULIS, A. (1991) Probability, Random Variables, and Stochastic Processes 3-d Ed. McGRAW-HILL, Inc.
PRICE, R. (1965) A Useful Theorem for Nonlinear Devices Having Gaussian Inputs. IRE, PGIT, Vol. IT-4.
RENYI, A. (1959) On Measures of Dependence. Acta Math. Acad. Sci. Hungar., 10, pp. 441-451.
STOYANOV, J. (1998) Global Dependency Measure for Sers of Random Elements "The Italian Problem" and Some Consequences. In: 1. Karatzas, B. S. Rajput. M.S. Taqqu (eds) Stochastic Processes and Relared Topics. Birkhäuser, pp. 357-375.