The Cambanis family of bivariate distributions: Properties and applications
DOI:
https://doi.org/10.6092/issn.1973-2201/6159Keywords:
Bivariate Cambanis family, association measures, total positivity, bivariate hazard rates, bivariate mean residual life, series and parallel systemsAbstract
The Cambanis family of bivariate distributions was introduced as a generalization of the Farlie-Gumbel-Morgenstern system. The present work is an attempt to investigate the distributional characteristics and applications of the family. We derive various coecients of association, dependence concepts and time-dependent measures. Bivariate reliability functions such as hazard rates and mean residual life functions are analysed. The application of the family as a model for bivariate lifetime data is also demonstrated.
References
C. AMBLARD, S. GIRARD (2009). A new extension of FGM copulas. Metrika, 70, 1–17.
J. E. ANDERSON, T. A. LOUIS, N. V. HOLM, B. HARVALD (1992). Timedependent association measures for bivariate survival distributions. Journal of the American Statistical Association, 87, 641–650.
I. BAIRAMOV, S. KOTZ, M. BEKCI (2001). New generalized Farlie-Gumbel-Morgenstern distributions and concomitants of order statistics. Journal of Applied Statistics, 28, 5, 521–536.
I. BAIRAMOV, S. KOTZ, T. J. KOZUBOWSKI (2003). A new measure of linear local dependence. Statistics, 37, 243–258.
A. P. BASU (1971). Bivariate failure rate. Jornal of American Statistical Association, 66, 103–104.
H. BEKRIZADEH, G. A. PARHAN, M. R. ZADKARMI (2012). A new generalization of Farlie-Gumbel-Morgenstern copulas. Applied Mathematical Sciences, 6, 71, 3527–3533.
S. BJERVE, K. DOKSUM (1993). Correlation curves: Measures of association as function of covariate values. The Annals of Statistics, 21, 890–902.
S. CAMBANIS (1977). Some properties and generalizations of Multivariate Eyraud-Gumbel-Morgenstern Distributions. Journal of Multivariate Analysis, 7, 551-559.
M. CARLES, C. M. CUDRAS, W. DAZ (2012). Another generaization of the bivariate FGM distribution with two- dimensional extensions. Acta Et Commentationes Universitatis Tartuinsis De Mathematica, 16, 1.
D. G. CLAYTON (1978). A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika, 65, 141–151.
D. DROUET MARI, S. KOTZ (2001). Correlation and Dependence. Imperial College Press, London.
J. A. GREENWOOD, J. M. LANDWEHR, N. C. MATALAS, J. R. WALLIS (1979). Probability weighted moments. Water Resources Research, 15, 1049–1054.
R. C. GUPTA (2003). On some association measures in bivariate distributions and their relationships. Journal of Statistical Planning and Inference, 117, 83–98.
R. C. GUPTA (2016). Reliability characteristics of Farlie-Gumbel-Morgenstern family of bivariate distributions. Communications in Statistics-Theory and Methods (to appear).
P. W. HOLLAND, Y. J. WANG (1987b). Dependence function for continuous bivariate densities. Communications in Statistics-Theory and Methods, 16, 863–876.
J. S. HUANG, S. KOTZ (1984). Correlation structure in iterated Farlie-Gumbel-Morgenstern distributions. Biometrika, 71, 633–636.
J. S. HUANG, S. KOTZ (1999). Modifications of the Farlie-Gumbel-Morgenstern distributions, A tough hill to climb. Metrika, 49, 135–145.
N. L. JOHNSON, S. KOTZ (1972). Distributions in statistics,Continuous Multivariate Distributions, John Wiley, Newyork.
A. JUSTEL, D. PENA, R. ZAMAR (1997). A multivariate Kolmogorov – Smirnov test of goodness of fit. Statistics and Probability letters, 35, 251–259.
J. P. KLEIN, M. L. MOESCHBERGER (1997). Survival Analysis Technique for censored and truncated data, Springer, New York.
S. KOTZ, N. L. JOHNSON (1977). Dependence properties of iterated generalized bivariate Farlie-Gumbel-Morgenstern distributions. Comptes, Rendus Academic Science, Paris, 285 A, 277–280.
N. U. NAIR, M. PREETH (2009). On some properties of equilibrium distributions of order n. Statistical methods Appl, 18, 453–464.
R. B. NELSON (2006). An introduction to copulas. (Second edition), Springer, New York.
W. SCHUANY, W. C. PARR, J. E. BOYER (1978). Correlation structure in Farlie-Gumbel-Morgenstern distributions. Biometrika, 65, 650–653.
M. SHAKED (1977). A family of concepts of dependence for bivariate distributions. Journal of the American Statistical Association, 72, 642–650.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2016 Statistica
Copyrights and publishing rights of all the texts on this journal belong to the respective authors without restrictions.
This journal is licensed under a Creative Commons Attribution 4.0 International License (full legal code).
See also our Open Access Policy.
