Characterizations of a family of bivariate Pareto distributions

Authors

  • Paduthol Godan Sankaran Cochin University of Science and Technology
  • N. Unnikrishnan Nair Cochin University of Science and Technology
  • Preethi John Cochin University of Science and Technology

DOI:

https://doi.org/10.6092/issn.1973-2201/6099

Keywords:

Bivariate Pareto distributions, characterization, dullness property, income gap ratio, generalized failure rate

Abstract

In the present paper, we study properties of a family of bivariate Pareto distributions. The well known dullness property of the univariate Pareto model is extended to the bivariate setup. Two measures of income inequality viz. income gap ratio and mean left proportional residual income are defined in the bivariate case. We also introduce bivariate generalized failure rate useful in reliability analysis. Characterizations, using the above concepts, for various members of the family of bivariate Pareto distributions are derived.

References

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.

T. ARTIKIS, A. VOUDOURI, M. MALLIARIS (1994). Certain selecting and underreporting processes. Mathematical and Computer Modelling, 20, pp. 103–106.

N. BALAKRISHNAN, C. D. LAI (2009). Continuous Bivariate Distributions. Springer, New York.

F. BELZUNCE, J. CANDEL, J. M. RUIZ (1998). Ordering and asymptotic properties of residual income distributions. Sankhy¯a, Series B, pp. 331–348.

D. D. HANAGAL (1996). A multivariate Pareto distribution. Communications in

Statistics-Theory and Methods, 25, pp. 1471–1488.

T. P. HUTCHINSON, C. D. LAI (1990). Continuous Bivariate Distributions, Emphasising Applications. Rumsby Scientific Publishing, Adelaide.

R. KORWAR (1985). On the joint characterization of distributions of true income and the proportion of reported income to the true income through a model of underreported incomes. Statistics and Probability Letters, 3, pp. 201–203.

H. LANGSETH (2002). Bayesian Networks with Applications in Reliability analysis. Ph.D. thesis, Norwegian University of Science and Technology, Guntur, India.

M. A. LARIVIERE (2006). A note on probability distributions with increasing generalized failure rates. Operations Research, 54, pp. 602–604.

M. A. LARIVIERE, E. L. PORTEUS (2001). Selling to the newsvendor: An analysis of price-only contracts. Manufacturing & Service Operations Management, 3, pp. 293–305.

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.

K. V. MARDIA (1962). Multivariate Pareto distributions. The Annals of Mathematical Statistics, 33, pp. 1008–1015.

S. NADARAJAH (2009). Models for over reported income. Applied Economics Letters, 16, pp. 699–703.

K. R. M. NAIR, N. U. NAIR (1989). Bivariate mean residual life. IEEE Transactions on Reliability, 38, pp. 362–364.

T. PHAM-GIA, N. TURKKAN (1997). Change in income distribution in the presence of reporting errors. Mathematical and Computer Modelling, 25, pp. 33–42.

P. G. SANKARAN, D. KUNDU (2014). A bivariate Pareto model, Statistics. p. DOI:10.1080/02331888.2012.719521.

P. G. SANKARAN, N. U. NAIR (1993). A bivariate Pareto model and its applications to reliability. Naval Research Logistics, 40, pp. 1013–1020.

P. G. SANKARAN, N. U. NAIR, J. PREETHI (2014). A family of bivariate pareto distributions. Statistica, 74, pp. 199–215.

P. K. SEN (1988). The harmonic Gini coefficient and affluence indexes. Mathematical Social Sciences, 16, pp. 65–76.

S. K. SINGH, G. S. MADDALA (1976). A function for size distribution of incomes. Econometrica, 44, pp. 963–970.

S. TALWALKER (1980). On the property of dullness of Pareto distribution. Metrika , 27, pp. 115–119.

W. Wong (1982). On the property of dullness of Pareto distribution. Tech. rep., Purdue University.

E. XEKALAKI (1983). A property of the Yule distribution and its applications. Communications in Statistics-Theory and Methods, 12, pp. 1181–1189.

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Published

2015-09-30

How to Cite

Sankaran, P. G., Nair, N. U., & John, P. (2015). Characterizations of a family of bivariate Pareto distributions. Statistica, 75(3), 275–290. https://doi.org/10.6092/issn.1973-2201/6099

Issue

Vol. 75 No. 3 (2015)

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Articles

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