Characterizations of some bivariate models using reciprocal coordinate subtangents
DOI:
https://doi.org/10.6092/issn.1973-2201/4995Keywords:
Reciprocal coordinate subtangent, Reliability measures, Characterizations, Conditionally specified modelsAbstract
In the present paper, we consider the bivariate version of reciprocal coordinate subtangent (RCST) and study its usefulness in characterizing some important bivariate models. In particular, characterization results are proved for a general bivariate model whose conditional distributions are proportional hazard rate models (see Navarro and Sarabia, 2011), Sarmanov family and Ali-Mikhail-Haq family of bivariate distributions. We also study the relationship between local dependence function and reciprocal subtangent and a characterization result is proved for a bivariate model proposed by Jones (1998). Further, the concept of reciprocal coordinate subtangent is extended to conditionally specified models.
References
B. C. ARNOLD (1995). Conditional survival models. In: N. BALAKRISHNAN (Ed.), Recent Advances in Life-Testing and Reliability, CRC Press, Boca Raton, FL.
B.C. ARNOLD (1996). Marginally and conditionally specified multivariate survival models. In: S. GHOSH, W. SCHUCANY, W. SMITH (Eds.), Statistics and Quality, Marcel Dekker, New York.
B. C. ARNOLD, D. STRAUSS (1988). Bivariate distributions with exponential conditionals. Journal of the American Statistical Association, 83, pp. 522-527.
B. C. ARNOLD, E. CASTILLO, J.M. SARABIA (1999). Conditional Specification of Statistical Models. New York, Springer.
B. C. ARNOLD, Y.H. KIM (1996). Conditional proportional hazard models. In: N. P. JEWELL, A. C. KIMBER, M. L. T. LEE, G. A. WHITMORE (Eds.). Lifetime Data: Models in Reliability and Survival Analysis. Kluwer Academic, Dordrecht, Netherlands.
C. D. LAI, M. XIE (2006). Stochastic Ageing and Dependence for Reliability. Springer, New York.
D. ROY, R. ROY (2010). Characterizations of bivariate and multivariate life distributions based on reciprocal subtangent. Communications in Statistics–Theory and Methods, 39, pp. 158-169.
I. BAIRAMOV, S. KOTZ, M. BEKCI (2001). New generalized Farlie-Gumbel-Morgenstern distributions and concomitants of order statistics. Journal of Applied Statistics, 28, no. 5, pp.521-536.
J. HAJEK, Z. SIDAK (1967). Theory of Rank Tests. Academic Press, pp. 15-17.
J. MI (2004). A general approach to the shape of failure rate and MRL functions. Naval Research Logistics, 51, pp. 543-556.
J. NAVARRO (2008). Likelihood ratio ordering of order statistics, mixtures and systems. Journal of Statistical Planning and Inference, 138, no. 5, pp. 1242-1257.
J. NAVARRO, J. M. SARABIA (2010). Alternative definitions of bivariate equilibrium Distributions. Journal of Statistical Planning and Inference, 140, pp. 2046-2056.
J. NAVARRO, J. M. SARABIA (2011). Reliability properties of bivariate conditional proportional hazard rates models. Journal of Multivariate Analysis, Published online first: doi:10.1016/j.jmva.2011.03.009.
J. NAVARRO, P. J. HERNANDEZ (2004). How to obtain bathtub-shaped failure rate models from normal mixtures. Probability in the Engineering and Informational Sciences, 18, pp. 511-531.
J. NAVARRO, S. M. SUNOJ, M. N. LINU (2011). Characterizations of bivariate models using dynamic Kullback–Leibler discrimination measures. Statistics and Probability Letters, 81, pp. 1594-1598.
J. M. RUIZ, J. NAVARRO (1994). Characterization of distributions by relationships between failure rate and mean residual life. IEEE Transactions on Reliability, 43, no. 4, pp. 640-644.
M. ASADI (1998). Characterization of Pearson system of distributions based on reliability measures. Statistical Papers, 39, pp. 347-360.
M. M. ALI, N. N. MIKHAIL, M. S. HAQ (1978). A class of bivariate distributions including the bivariate logistics. Journal of multivariate analysis, 8, pp. 405-412.
M. C. JONES (1998). Constant local dependence function. Journal of Multivariate Analysis, 64, pp. 148-155.
M. L. T. LEE (1996). Properties and applications of the Sarmanov family of bivariate distributions. Communications in Statistics–Theory and Methods, 25, pp. 1207-1222.
N. U. NAIR, P. G. SANKARAN (1991). Characterization of Pearson family of distributions. IEEE Transactions on Reliability, 40, pp. 75-77.
P. G. SANKARAN, N. U. NAIR (2000). On some reliability aspects of Pearson family of distributions. Statistical Papers, 41, pp. 109-117.
P. G. SANKARAN, S. M. SUNOJ (2004). Identification of models using failure rate and mean residual life of doubly truncated random variables. Statistical Papers, 45, pp. 97-109.
P. K. WILLETT, J. B. THOMAS (1985). A simple bivariate density representation. In: Proceedings of the 23rd Annual Allertan Conference on Communicating Control and Computing. Coordinated Science Laboratory and Department of Electrical and Computer Engineering. University of Illinois, Urbana-Champaign, pp. 888-897.
P. K. WILLETT, J. B. THOMAS (1987). Mixture models for underwater burst noise and their relationship to simple bivariate density representation. IEEE Journal of Oceanic Engineering, 12, pp. 29-37.
P. W. HOLLAND, Y. J. WANG (1987). Dependence function for continuous bivariate densities. Communications in Statistics–Theory and Methods, 16, pp. 863-876.
R. C. GUPTA, R. WARREN (2001). Determination of change points of nonmonotonic failure rates. Communications in Statistics-Theory and Methods, 30, pp. 1903–1920.
R. E. GLASER (1980). Bathtub and related failure rate characterizations. Journal of the American Statistical Association, 75, pp. 667-672.
S. M. SUNOJ, T. B. SREEJITH (2012). Some results on reciprocal subtangent in the context of weighted models. Communications in Statistics-Theory and Methods, 41, no. 8, pp. 1397-1410.
S. P. MUKHERJEE, D. ROY (1989). Properties of classes of probability distributions based on the concept of reciprocal coordinate subtangent. Calcutta Statistical Association Bulletin, 38, pp. 169-180.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2014 Statistica
This journal is licensed under a Creative Commons Attribution 3.0 Unported License (full legal code).
Authors accept to transfer their copyrights to the journal.
See also our Open Access Policy.
