Birleşik Normal Rastgele Değişkenler İçin Korelasyonsuzluk Kümeleri
Yıl 2003,
Cilt: 2 Sayı: 2, 1 - 5, 17.08.2003
Svetlana Gadetska
Sofia Ostrovska
Öz
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.
Kaynakça
- 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
Yıl 2003,
Cilt: 2 Sayı: 2, 1 - 5, 17.08.2003
Svetlana Gadetska
Sofia Ostrovska
Öz
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.
Kaynakça
- 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.