Abstract
In this paper, we consider a family of bivariate distributions which is a generalization of the Morgenstern family of bivariate distributions. We have derived some properties of concomitants of record values which characterize this generalized class of distributions. The role of concomitants of record values in the unique determination of the parent bivariate distribution has been established. We have also derived properties of concomitants of record values which characterize each of the following families viz Morgenstern family, bivariate Pareto family and a generalized Gumbel’s family of bivariate distributions. Some applications of the characterization results are discussed and important conclusions based on the characterization results are drawn.
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References
Ahsanullah M (2004) Record values from uniform distribution. Int J Stat Sci 3:17–22
Ahsanullah M, Nevzorov VB (2000) Some distributions of induced record values. Biometrical J 42: 1069–1081
Arnold BC, Balakrishnan N, Nagaraja HN (1998) Records. Wiley, New York
Chacko M (2007) Unpublished Ph.D. Thesis. University of Kerala, Trivandrum
Chacko M, Thomas PY (2006) Concomitants of record values arising from Morgenstern type bivariate logistic distribution and some of their applications in parameter estimation. Metrika 64:317–331
Chacko M, Thomas PY (2008) Estimation of parameters of bivariate normal distribution using concomitants of record values. Stat Pap 49:263–275
Chandler KN (1952) The distribution and frequency of record values. J R Stat Soc Ser B 14:220–228
David HA, Nagaraja HN (1998) Concomitants of order statistics, handbook of statistics, vol 16. North-Holland, Amsterdam, pp 487–513
David HA, Nagaraja HN (2003) Order statistics, 3rd edn. Wiley, New York
Houchens RL (1984) Record value theory and inference, Ph.D. Dissertation, University of California, Riverside, CA
Rao CR, Shanbhag DN (1998) Recent approaches to characterizations based on order statistics and record values. In: Balakrishnan N, Rao CR (eds) Handbook of statistics, vol 16. North-Holland, Amsterdam, pp 231–256
Thomas PY, Veena TG (2011) On an application of concomitants of order statistics in characterizing a family of bivariate distributions. Commun Stat Theory Methods 40:1445–1452
Veena TG, Thomas PY (2008) Characterizations of bivariate distributions by properties of concomitants of order statistics. Stat Probab Lett 78:3350–3354
Acknowledgments
The authors wish to thank the referee for the valuable and creative comments and suggestions which helped much in the presentation of the paper in its present form. The first author acknowledges his gratefulness to University Grants Commission, Government of India for providing financial assistance in the form of UGC-Emeritus Fellowship. The second author is much grateful to the CSIR for the financial support received for this research work in the form of CSIR-JRF.
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Thomas, P.Y., Veena, T.G. Characterizations of bivariate distributions using concomitants of record values. Metrika 77, 947–963 (2014). https://doi.org/10.1007/s00184-013-0480-6
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DOI: https://doi.org/10.1007/s00184-013-0480-6