A family of bivariate Pareto distributions
DOI:
https://doi.org/10.6092/issn.1973-2201/5001Keywords:
bivariate Pareto distribution, correlation coefficient, association measures, dullness propertyAbstract
Pareto distributions have been extensively used in literature for modelling and analysis of income and lifetime data. In the present paper, we introduce a family of bivariate Pareto distributions using a generalized version of dullness property. Some important bivariate Pareto distributions are derived as special cases. Distributional properties of the family are studied. The dependency structure of the family is investigated. Finally, the family of distributions is applied to two real life data situation.References
M. Abramowitz, I. A. Stegun (1966). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. US Government Printing Office.
J. E. Anderson, T. A. Louis, N. V. Holm, B. Harvald (1992). Time-dependent association measures for bivariate survival distributions. Journal of the American Statistical Association, 87, pp. 641–650.
B. C. Arnold (1985). Pareto Distribution. Wiley, New York.
B. C. Arnold (1990). A flexible family of multivariate Pareto distributions. Journal of Statistical Planning and Inference, 24, pp. 249–258.
B. C. Arnold (1992). Conditionally Specified Distributions. Springer, New York.
N. Balakrishnan, C. Lai (2009). Continuous Bivariate Distributions. Springer, New York.
R. E. Barlow, M. B. Mendel (1992). De finetti-type representations for life distributions. Journal of the American Statistical Association, 87, pp. 1116–1122.
R. E. Barlow, F. Proschan (1975). Statistical Theory of Reliability and Life Testing: Probability Models. Holt, Rinehart and Winston,New York.
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, pp. 141–151.
S. Csörgá, A. Welsh (1989). Testing for exponential and Marshall–Olkin distributions. Journal of Statistical Planning and Inference, 23, pp. 287–300.
R. C. Gupta (2003). On some association measures in bivariate distributions and their relationships. Journal of Statistical Planning and Inference, 117, pp. 83–98.
H. Joe (1997). Multivariate Models and Dependence Concepts. CRC Press.
H. Joe (2005). Asymptotic efficiency of the two-stage estimation method for copula-based models. Journal of Multivariate Analysis, 94, pp. 401–419.
N. L. Johnson, S. Kotz, N. Balakrishnan (1994). Continuous Univariate Distributions. John Wiley and Sons, New York.
A. Justel, D. Pe~na, R. Zamar (1997). A multivariate Kolmogorov-Smirnov test of goodness of fit. Statistics and Probability Letters, 35, pp. 251–259.
Y. Kagan, Linnik, C. R. Rao, B. Ramachandran (1973). Characterization Problems in Mathematical Statistics. Wiley, New York.
W. Kibble (1941). A two-variate gamma type distribution. Sankhy¯a, Series A, 5, pp. 137–150.
H. Kim, P. H. Kvam (2004). Reliability estimation based on system data with an unknown load share rule. Lifetime Data Analysis, 10, pp. 83–94.
S. Kotz, N. Balakrishnan, N. L. Johnson (2002). Continuous Multivariate Distributions. John Wiley and Sons, New York.
H. Langseth (2002). Bayesian networks with applications in reliability analysis. Ph.D. thesis, Norwegian University of Science and Technology, Guntur, India.
D. V. Lindley, N. D. Singpurwalla (1986). Multivariate distributions for the life lengths of components of a system sharing a common environment. Journal of Applied Probability, pp. 418–431.
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