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Some Results on Weighted Distributions for Positive-Valued Random Variables

Published online by Cambridge University Press:  27 July 2009

S. C. Kochar  and
R. P. Gupta
S. C. Kochar
Affiliation:
Department of StatisticsPanjab University Chandigarh, India
R. P. Gupta
Affiliation:
Department of Mathematics, Statistics, and Computer Science Dalhousie University, Halifax, N.S. Canada B3H 3J5
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Abstract

For nonnegative random variables, the weighted distributions have been compared with the original distributions with the help of partial orderings of probability distributions. Bounds on the moments of the weighted distributions have been obtained in terms of the moments of the original distributions for some nonparametric classes of aging distributions.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 1 , Issue 4 , October 1987 , pp. 417 - 423
Copyright
Copyright © Cambridge University Press 1987

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References

Bagai, I. & Kochar, S.C. (1986). On tail-ordering and comparison of failure rates. Commun. Statist. Theor. Meth. 15(4): 1377–1388.CrossRefGoogle Scholar
Barlow, R.E. & Proschan, F. (1981). Statistical theory of reliability and life testing. Maryland: To Begin With.Google Scholar
Blumenthal, S. (1971). Proportional sampling in life length studies. Technometrics 9: 205–218.CrossRefGoogle Scholar
Cox, D.R. (1969). Some sampling problems in technology. In Johnson, N. L. (ed), New developments in survey sampling. NY: Wiley-lnterscience.Google Scholar
Deshpande, J.V. & Kochar, S.C. (1983). Dispersive ordering is the same as tail-ordering. Adv. Appl. Prob. 15: 686–687.Google Scholar
Deshpande, J.V., Kochar, S.C., & Singh, H. (1986). Aspects of positive aging. J. Appl. Prob., 23: 748–758.CrossRefGoogle Scholar
Gupta, R.C. (1986). Relations for reliability measures under length-biased sampling. Scand. J. Statist. 13: 49–56.Google Scholar
Hollander, M. & Proschan, F. (1984). Nonparametric concepts and methods in reliability. Handbook of statistics, Vol. 4, Nonparametric methods, edited by Krishnaiah, P.R. and Sen, P. K., pp. 613–655.Google Scholar
Mahfoud, M. & Patil, G.P. (1982). On weighted distributions. In Kallianpur, G. et al. (eds.), In Statistics and Probability Essays in Honor of C.R. Rao. Amsterdam: North-Holland Publishing Company, pp. 479–492.Google Scholar
Patil, G.P. & Rao, C.R. (1977). Weighted distributions: A survey of their applications. In Krishnaiah, P.R. (ed), Applications of Statistics. Amsterdam: North Holland Publishing Company, pp. 383–405.Google Scholar
Patil, G.P. & Rao, C.R. (1978). Weighted distributions and size-biased sampling with applications to wildlife populations and human families. Biometrics 34: 179–189.CrossRefGoogle Scholar
Rao, C.R. (1965). On discrete distributions arising out of ascertainment: What population does a sample represent? In Atkinson, A.C. & Fienberg, S.E. (eds.), Celebration of Statistics, The 151 Centenary Volume, Chapter 24, pp. 543–569.Google Scholar
Ross, S.M.Stochastic processes. Wiley, New York, 1983.Google Scholar
Schaeffer, R.L. (1972). Size-biased sampling. Technometrics 14: 635–644.CrossRefGoogle Scholar
Shaked, M. (1982). Dispersive ordering of distributions. J. Appl. Prob. 19: 310–320.CrossRefGoogle Scholar