Transfer of Global Measures of Dependence into Cumulative Local
Affiliation(s)
Kettering University, Flint, USA. sahib_esa@yahoo.com. University of Sao Paulo, Sao Paulo, Brazil. University of Piraeus, Piraeus, Greece.
Kettering University, Flint, USA. sahib_esa@yahoo.com. University of Sao Paulo, Sao Paulo, Brazil. University of Piraeus, Piraeus, Greece.
ABSTRACT
We explore an idea of transferring some classic measures of global dependence between random variables Χ1, Χ2, L, Χn into cumulative measures of dependence relative at any point (χ1, χ2, L, χn) in the sample space. It allows studying the behavior of these measures throughout the sample space, and better understanding and use of dependence. Some examples on popular copula distributions are also provided.
Cite this paper
Dimitrov, B. , Esa, S. , Kolev, N. and Pitselis, G. (2014) Transfer of Global Measures of Dependence into Cumulative Local. Applied Mathematics, 5, 615-627. doi: 10.4236/am.2014.54058.
Dimitrov, B. , Esa, S. , Kolev, N. and Pitselis, G. (2014) Transfer of Global Measures of Dependence into Cumulative Local. Applied Mathematics, 5, 615-627. doi: 10.4236/am.2014.54058.
References
[1] Cooke, R.M., Morales, O. and Kurowitcka, D. (2007) Vine in Overview. Proceedings of 3rd Brazilian Conference on Statist. Modeling in Insurance and Finance, 26-30 March 2007, 2-20. [2] Dimitrovm B. (2010) Some Obreshkov Measures of Dependence and Their Use. Compte Rendus de l’Academie Bulgare des Sciences, 63, 15-18. [3] Bradley, R.C. (2005) Basic Properties of Strong Mixing Conditions. A Survey and Some Open Questions. Probability Surveys, 2, 107-104. [4] Genest, C. and Boies, J. (2003) Testing Dependence with Kendall Plots. The American Statistician, 44, 275-284.
http://dx.doi.org/10.1198/0003130032431 [5] Obreshkov, N. (1963) Probability Theory. Nauka i Izkustvo, Sofia (in Bulgarian). [6] Dimitrov, B., Kolev, N. and Goncalves, M. (2007) Some Measures of Dependence between Two Random Variables. Work Paper. [7] Renyi, A. (1969) Foundations of Probability Theory. Holden-Day, San Francisco. [8] Nelsen, R. (1999) An Introduction to Copulas. Springer, New York. http://dx.doi.org/10.1007/978-1-4757-3076-0 [9] Kocherlakota, S. (1988) On the Compounded Bivariate Poisson Distribution: A Unified Treatment. Annals of the Institute of Statistical Mathematics, 49, 61-70. http://dx.doi.org/10.1007/BF00053955
[1] Cooke, R.M., Morales, O. and Kurowitcka, D. (2007) Vine in Overview. Proceedings of 3rd Brazilian Conference on Statist. Modeling in Insurance and Finance, 26-30 March 2007, 2-20. [2] Dimitrovm B. (2010) Some Obreshkov Measures of Dependence and Their Use. Compte Rendus de l’Academie Bulgare des Sciences, 63, 15-18. [3] Bradley, R.C. (2005) Basic Properties of Strong Mixing Conditions. A Survey and Some Open Questions. Probability Surveys, 2, 107-104. [4] Genest, C. and Boies, J. (2003) Testing Dependence with Kendall Plots. The American Statistician, 44, 275-284.
http://dx.doi.org/10.1198/0003130032431 [5] Obreshkov, N. (1963) Probability Theory. Nauka i Izkustvo, Sofia (in Bulgarian). [6] Dimitrov, B., Kolev, N. and Goncalves, M. (2007) Some Measures of Dependence between Two Random Variables. Work Paper. [7] Renyi, A. (1969) Foundations of Probability Theory. Holden-Day, San Francisco. [8] Nelsen, R. (1999) An Introduction to Copulas. Springer, New York. http://dx.doi.org/10.1007/978-1-4757-3076-0 [9] Kocherlakota, S. (1988) On the Compounded Bivariate Poisson Distribution: A Unified Treatment. Annals of the Institute of Statistical Mathematics, 49, 61-70. http://dx.doi.org/10.1007/BF00053955