Browse > Article
http://dx.doi.org/10.5351/CKSS.2008.15.2.193

Aspects of Dependence in Lomax Distribution  

Asadian, N. (Department of Statistics, Faculty of Mathematics Sciences, Ferdowsi University of Mashhad)
Amini, M. (Department of Statistics, Faculty of Mathematics Sciences, Ferdowsi University of Mashhad)
Bozorgnia, A. (Department of Statistics, Faculty of Mathematics Sciences, Ferdowsi University of Mashhad)
Publication Information
Communications for Statistical Applications and Methods / v.15, no.2, 2008 , pp. 193-204 More about this Journal
Abstract
In this paper we study some positive dependence concepts, introduced by Caperaa and Genest (1990) and Shaked (1977b), for bivariate lomax distribution. In particular, we obtain some measures of association for this distribution and derive the tail-dependence coefficients by using copula function. We also compare Spearman's $\rho_s$ with Kendall's $\tau$ for bivariate lomax distribution.
Keywords
Bivariate lomax distribution; positive quadrant dependence; dependent by total positivity of order two; decreasing failure rate; copula; tail dependence of coefficient;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Johnson N. L. and Kotz, S. (1975). A vector valued multivariate hazard rate. Journal of Multivariate Analysis, 5, 53-66   DOI
2 Karlin, S. (1968). Total Positivity. Stanford University Press, California
3 Lehmann, E. L. (1966). Some concepts of dependence. The Annals of Mathematical Statistis, 37, 1137-1153   DOI
4 Shaked, M. (1977b). A family of concept of dependence for bivariate distributions. Journal of the American Statistical Association, 72, 642-650   DOI
5 Winterbottom, A. (1984). The interval estimation of system reliability from component test data. Operation Research, 32, 628-640   DOI   ScienceOn
6 Lindley, D.V. and Singpurwalla, N.D. (1986). Multivariate distributions for the life lengths of component of a system sharing a common environment. Journal of Applied Probability, 23, 418-431   DOI   ScienceOn
7 Nayak, T. K. (1987). Multivariate lomax distribution: Properties and usefulness in reliability theory. Journal of Applied Probability, 24, 170-177   DOI   ScienceOn
8 Nelsen, R. B. (1999). An Intruduction to Copulas. Springer-Verlag Berlin and Heidel- berg GmbH & Co. KG, New-York
9 Clayton, D. G. (1978). A model for association in bivariate life tables and its appli- cation in epidemiological studies of familial tendency in chronic disease incidence. Biometrika, 65, 141-151   DOI   ScienceOn
10 Drouet, Mari, D. and Kotz, S. (2001). Correlation and Dependence. Imperial College Press, London
11 Frahm, G. (2006). On the extremal dependence coefficient of multivariate distributions. Statistics & Probability Letters, 76, 1470-1481   DOI   ScienceOn
12 Fredricks, G. A. and Nelsen, R. B. (2007). On the relationship between Spearman's rho and Kendall's tau for pairs of continuous random variables. Journal of Statistical Planning and Inference, 137, 2143-2150   DOI   ScienceOn
13 Brindley, Jr., E. C. and Thompson, Jr., W. A. (1972). Dependence and aging aspects of multivariate survival. Journal of the American Statistical Association, 67, 822-830   DOI
14 Arnold, B. C. and Zahedi, H. (1988). On multivariate mean remaining life functions. Journal of Multivariate Analysis, 25, 1-9   DOI
15 Gupta, R. C. (2003). On some association measures in bivariate distributions and their relationships. Journal of Statistical Planning and Inference, 117, 83-98   DOI   ScienceOn
16 Oakes, D. (1989). Bivariate survival models induced by frailties. Journal of the American Statistical Association, 84, 487-493   DOI
17 Shaked, M. (1977a). A concept of positive dependence for exchangeable random variables. Annals of Statistics, 5, 505-515   DOI
18 Barlow, R. E. and Proschan, F. (1975). Statistical Theory of Reliability and Life Testing: Probability Models. Holt, Rinehart and Winston, New York
19 Basu, A. P. (1971). Bivariate failure rate. Journal of the American Statistical Association, 66, 103-104   DOI
20 Caperaa, P. and Genest, C. (1990). Concepts de dendance et ordres stochastiques pour des lois bidimensionnelles. The Canadian Journal of Statistics, 18, 315-326   DOI
21 Harris, R. (1970). A multivariate definition for increasing hazard rate distribution functions. The Annals of Mathematical Statistis, 41, 713-717   DOI
22 Nadarjah, S. (2005). Sums, products and ratios for the bivariate lomax distribution. Computational Statistics & Data Analysis, 49, 109-129   DOI   ScienceOn