Some weighted distribution results on univariate and bivariate cases

Journal of Statistical Planning and Inference

Volumn 77, Issue 2, 1999, Pages 169-180

  Nanda, Asok K ^a   Jain, Kanchan ^a  

^a PANJAB UNIVERSITY   (India)

Author keywords

62N; Equilibrium distributions; Length biased distributions; Likelihood ratio dependence; Partial orderings; Quadrant dependence; Right tail increasing; TP2 and RR2 functions

Indexed keywords

EID: 0347504524     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-3758(98)00190-6     Document Type: Article

References (25)

1. Arnold, B.C., Nagaraja, H.N., 1991. On some properties of bivariate weighted distributions. Comm. Statist. Theory Meth. 20 (5 & 6), 1853-1860.
2. Barlow, R.E., Proschan, F., 1975. Statistical Theory of Reliability and Life Testing: Probability Models. Holt, Rinehart and Winston, New York.
3. Block, H.W., Savits, T.H., 1980. Laplace transforms for classes of life distributions. Ann. Probab. 8 (3), 465-474.
4. Blumenthal, S., 1963. Proportional sampling in life length studies. Technometrics 9 (2), 205-218.
5. Cnaan, A., 1985. Survival models with two phases and length biased sampling. Comm. Statist. 14 (4), 861-886.
6. Cox, D.R., 1962. Renewal Theory. Spottiswoode, Ballantyne and Company, London.
7. Deshpande J.V., Kochar S.C., Singh H. Aspects of positive ageing. J. Appl. Probab. 23:1986;748-758.
8. Ebrahimi, N., Ghosh, M., 1981. Multivariate negative dependence. Comm. Statist. Theory Meth. A 10 (4), 307-337.
9. Fisher R.A. The effects of methods of ascertainment upon the estimation of frequencies. Ann. Eugenics. 6:1934;13-25.
10. Gupta R.C. On the monotonic properties of the residual variance and their applications in reliability. J. Statist. Plann. Inference. 16:1987;329-335.
11. Gupta, R.C., Kirmani, S.N.U.A., 1990. The role of weighted distributions in stochastic modeling. Comm. Statist. Theory Meth. 19 (9), 3147-3162.
12. Jain, K., Nanda, A.K., 1995. On multivariate weighted distributions. Comm. Statist. Theory Meth. 24 (10), 2517-2539.
13. Jain, K., Singh, H., Bagai, I., 1989. Relations for reliability measures of weighted distributions. Comm. Statist. Theory Meth. 18 (12), 4393-4412.
14. Karlin S., Proschan F. Polya type distributions of convolutions. Ann. Math. Statist. 31:1962;721-736.
15. Karlin S., Rinott Y. Classes of orderings of measures and related correlation inequalities II. Multivariate reverse rule distributions. J. Multivariate Anal. 10:1980;499-516.
16. Kumar, J.D., Proschan, F., 1983. Negative association of random variables with applications. Ann. Statist. 11 (1), 286-295.
17. Lehmann E.L. Some concepts of positive dependence. Ann. Math. Statist. 37:1966;1137-1153.
18. Mahfoud, M., Patil, G.P., 1982. On weighted distributions. In: Kallianpur, G., Krishnaiah, P.R., Ghosh, J.K. (Eds.), Statistics and Probability: Essays in Honor of C.R. Rao. North-Holland, Amsterdam, pp. 479-492.
19. Patil, G.P., Rao, C.R., 1977. In: Krishnaiah, P.R. (Ed.), The Weighted Distributions: A Survey and Their Applications. North-Holland, Amsterdam, pp. 383-405.
20. Patil G.P., Rao C.R. Weighted distributions and size-biased sampling with applications to wild-life populations and human families. Biometrics. 34:1978;179-189.
21. Rao, C.R., 1965. On discrete distributions arising out of methods of ascertainment. In: Patil, G.P. (Ed.), Classical and Contagious Discrete Distributions. Permagon Press, Oxford and Statistical Publishing Society, Calcutta, pp. 320-332.
22. Ross, S.M., 1983. Stochastic Processes. Wiley, New York.
23. Sen A., Khattree R. Length biased distribution, equilibrium distribution and characterization of probability laws. J. Appl. Statist. Sci. 3:1996;239-252.
24. Shaked, M., Shanthikumar, J.G., 1994. Stochastic Orders and their Applications. Academic Press, New York.
25. Zelen M., Feinleib M. On the theory of screening for chronic diseases. Biometrika. 56:1969;601-614.