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ON GENERALIZED SARMANOV BIVARIATE DISTRIBUTIONS

Year 2011, Volume 01, Issue 1, 86 - 97, 01.06.2011

Abstract

A class of bivariate distributions which generalizes the Sarmanov class is introduced. This class possesses a simple analytical form and desirable dependence properties. The admissible range for association parameter for given bivariate distributions are derived and the range for correlation coefficients are also presented.

References

  • Barlow R. and Proschan, F., (1981), Statistical Theory of Reliability and Life Testing: Probability Models, to begin with, Silver Spring, MD.
  • Bairamov, I.G., Kotz, S. and Bek¸ci, M., (2001), New generalized Farlie-Gumbel-Morgenstern distri- butions and concomitants of order statistics, Journal of Applied Statistics, 28(5), 521-536.
  • Bairamov, I.G. and Kotz, S. (2002) Dependence structure and symmetry of Huang-Kotz FGM distri- butions and their extensions. Metrika. 56 ,1, 55-72.
  • Bairamov, I. G., Kotz, S. and Gebizlioglu O.L. (2001) The Sarmanov family and its generalization. South African Statistical Journal. 35, 205-224.
  • Huang, J.S. and Kotz, S., (1999), Modifications of the Farlie-Gumbel-Morgenstern distributions, A tough hill to climb, Metrika, 49, 135-145.
  • Joe H., (1997), Multivariate Models and Dependence Concepts, Chapman and Hall, London.
  • Lee, M.-L. T., (1996), Properties and applications of the Sarmanov family of bivariate distributions, Communications in Statistics. -Theory Meth., 25(6), 1207-1222.
  • Lin, G.D. and Huang, J.S., (2011), Maximum correlation for the generalized Sarmanov bivariate distributions, Journal of Statistical Planning and Inference, 141, 2738-2749.
  • Nelsen, R.B., (1998), An Introduction to Copulas, Springer-Verlag, New York.
  • Sarmanov, O.V., (1966), Generalized normal correlation and two-dimensional Frechet classes, Doklady (Sovyet Mathematics), Tom 168, 596-599.
  • Shaked, M., Shanthikumar, J.G., (1994), Stochastic Orders and Their Applications, Academic Press. Boston.
  • Yu, S., Ouarda, T.B.M.J. and Bob´ee, B., (2001), A rewiew of bivariate gamma distributions for hydrological application, Journal of Hydrology, 246, 1-18.
  • Ismihan Bairamov is presently Professor of Mathematics and Statistics and Dean of Faculty of Arts and Sciences, Izmir University of Economics, Turkey. He graduated from Faculty of Applied Mathematics of Azerbaijan

Year 2011, Volume 01, Issue 1, 86 - 97, 01.06.2011

Abstract

References

  • Barlow R. and Proschan, F., (1981), Statistical Theory of Reliability and Life Testing: Probability Models, to begin with, Silver Spring, MD.
  • Bairamov, I.G., Kotz, S. and Bek¸ci, M., (2001), New generalized Farlie-Gumbel-Morgenstern distri- butions and concomitants of order statistics, Journal of Applied Statistics, 28(5), 521-536.
  • Bairamov, I.G. and Kotz, S. (2002) Dependence structure and symmetry of Huang-Kotz FGM distri- butions and their extensions. Metrika. 56 ,1, 55-72.
  • Bairamov, I. G., Kotz, S. and Gebizlioglu O.L. (2001) The Sarmanov family and its generalization. South African Statistical Journal. 35, 205-224.
  • Huang, J.S. and Kotz, S., (1999), Modifications of the Farlie-Gumbel-Morgenstern distributions, A tough hill to climb, Metrika, 49, 135-145.
  • Joe H., (1997), Multivariate Models and Dependence Concepts, Chapman and Hall, London.
  • Lee, M.-L. T., (1996), Properties and applications of the Sarmanov family of bivariate distributions, Communications in Statistics. -Theory Meth., 25(6), 1207-1222.
  • Lin, G.D. and Huang, J.S., (2011), Maximum correlation for the generalized Sarmanov bivariate distributions, Journal of Statistical Planning and Inference, 141, 2738-2749.
  • Nelsen, R.B., (1998), An Introduction to Copulas, Springer-Verlag, New York.
  • Sarmanov, O.V., (1966), Generalized normal correlation and two-dimensional Frechet classes, Doklady (Sovyet Mathematics), Tom 168, 596-599.
  • Shaked, M., Shanthikumar, J.G., (1994), Stochastic Orders and Their Applications, Academic Press. Boston.
  • Yu, S., Ouarda, T.B.M.J. and Bob´ee, B., (2001), A rewiew of bivariate gamma distributions for hydrological application, Journal of Hydrology, 246, 1-18.
  • Ismihan Bairamov is presently Professor of Mathematics and Statistics and Dean of Faculty of Arts and Sciences, Izmir University of Economics, Turkey. He graduated from Faculty of Applied Mathematics of Azerbaijan

Details

Primary Language English
Journal Section Research Article
Authors

Ismihan BAİRAMOV This is me
Izmir University of Economics, Department of Mathematics, 35330, Balcova, Izmir, Turkey


Banu ALTİNSOY This is me
Ministry of Transport and Communication of the Republic of Turkey, Department of Strategy and Development, Hakkı Turayli¸c Caddesi No:5 Emek, Ankara, Turkey


G. Jay KERNS This is me
Youngstown University, Department of Mathematics and Statistics, Youngstown, Ohio 44555-0002, USA

Publication Date June 1, 2011
Published in Issue Year 2011, Volume 01, Issue 1

Cite

Bibtex @ { twmsjaem761814, journal = {TWMS Journal of Applied and Engineering Mathematics}, issn = {2146-1147}, eissn = {2587-1013}, address = {Işık University ŞİLE KAMPÜSÜ Meşrutiyet Mahallesi, Üniversite Sokak No:2 Şile / İstanbul}, publisher = {Turkic World Mathematical Society}, year = {2011}, volume = {01}, number = {1}, pages = {86 - 97}, title = {ON GENERALIZED SARMANOV BIVARIATE DISTRIBUTIONS}, key = {cite}, author = {Bairamov, Ismihan and Altinsoy, Banu and Kerns, G. Jay} }