Abstract
The earlier concept of bivariate lack of memory property has been examined and an alternative concept of bivariate lack of memory property has been presented along with a set of equivalent conditions. In this process, the link relations known in the literature on univariate lack of memory property have been extended to the bivariate set-up. A multivariate extension of the lack of memory property has also been proposed.
Similar content being viewed by others
References
Block, H. W. (1977). A characterization of a bivariate exponential distribution, Ann. Statist., 5, 808–812.
Block, H. W. and Basu, A. P. (1974). A continuous bivariate exponential extension, J. Amer. Statist. Assoc., 69, 1031–1037.
Cowan, R. (1987). A bivariate exponential distribution arising in random geometry, Ann. Inst. Statist. Math., 39, 103–111.
Downton, F. (1970). Bivariate exponential distributions in reliability theory, J. Roy. Statist. Assoc. Ser. B, 32, 408–417.
Freund, R. J. (1961). A bivariate extension of the exponential distribution, J. Amer. Statist. Assoc., 56, 971–977.
Galambos, J. and Kotz, S. (1978). Characterizations of probability distributions, Springer, Berlin.
Gumble, E. J. (1960). Bivariate exponential distributions, J. Amer. Statist. Assoc., 55, 698–707.
Hawks, A. G. (1972). A bivariate exponential distribution with applications to reliability theory, J. Roy. Statist. Assoc. Ser. B, 34, 129–131.
Johnson, N. L. and Kotz, S. (1975). A vector-valued multivariate hazard rate, J. Multivariate Anal., 5, 53–66, (Addendum: ibid, (1975) 5, p. 498).
Krishnaji, N. (1971). Note on characterising property of the exponential distribution, Ann. Math. Statist., 42, 361–362.
Marshall, A. W. and Olkin, J. (1967). A multivariate exponential distribution, J. Amer. Statist. Assoc., 62, 30–44.
Mukherjee, S. P. and Roy, D. (1986). Some characterizations of the exponential and related life distributions, Calcutta Statist. Assoc. Bull., 35, 189–197.
Mukherjee, S. P. and Roy, D. (1996). Bivariate distributions through Cox's regression model, Frontiers in Probability and Statistics (eds. S. P. Mukherjee, S. K. Basu and B. K. Sinha), 290–300.
Muth, E. J. (1977). Reliability models with positive memory derived from the mean residual life, The Theory and Applications of Reliability, Vol II (ed. C. P. Tsokos and I. Shimi), 401–436, Academic Press, New York.
Roy, D. (1993). Reliability measures in the discrete bivariate set-up and related characterization results for a bivariate geometric distribution, J. Multivariate Anal., 46, 362–373.
Roy, D. and Gupta, R. P. (1996). Bivariate extension of Lomax and finite range distributions through characterization approach, J. Multivariate Anal., 59, 22–33.
Roy, D. and Mukherjee, S. P. (1989). Characterizations of some bivariate life distributios, J. Multivariate Anal., 28, 1–8.
Samanta, M. (1975). A characterization of the bivariate exponential distribution, J. Indian Soc. Agricultural Statist., 27, 67–70.
Sarkar, S. K. (1987). A continuous bivariate exponential ditribution, J. Amer. Statist. Assoc., 82, 667–675.
Zahedi, H. (1985). Some new classes of multivariate survival functions, J. Statist. Plann. Inference, 11, 171–188.
Author information
Authors and Affiliations
About this article
Cite this article
Roy, D. On Bivariate Lack of Memory Property and a New Definition. Annals of the Institute of Statistical Mathematics 54, 404–410 (2002). https://doi.org/10.1023/A:1022486321702
Issue Date:
DOI: https://doi.org/10.1023/A:1022486321702