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ON BOUNDS AND APPROXIMATING WEIGHTED DISTRIBUTIONS BY EXPONENTIAL DISTRIBUTIONS

Published online by Cambridge University Press:  01 June 2006

Broderick O. Oluyede
Broderick O. Oluyede
Affiliation:
Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA 30460, E-mail: boluyede@georgiasouthern.edu
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Abstract

In this article, we obtain error bounds for exponential approximations to the classes of weighted residual and equilibrium lifetime distributions with monotone weight functions. These bounds are obtained for the class of distributions with increasing (decreasing) hazard rate and mean residual life functions.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 20 , Issue 3 , July 2006 , pp. 517 - 528
Copyright
© 2006 Cambridge University Press

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References

REFERENCES

Barlow, R., Marshall, A.W., & Proschan, F. (1963). Properties of probability distributions with monotone hazard rate. Annals of Mathematical Statistics 34: 375–389.Google Scholar
Daniels, H.E. (1942). A new technique for the analysis of fiber length distribution in wool. Journal of Textile Institute 33: 137–150.Google Scholar
Gupta, R.C. & Keating, J.P. (1985). Relations for reliability measures under length-biased sampling. Scandinavian Journal of Statistics 13: 49–56.Google Scholar
Kijima, M. (1989). Some results for repairable systems with general repair. Journal of Applied Probability 26: 89–102.Google Scholar
Oluyede, B.O. (1999). On inequalities and selection of experiments for length-biased distributions. Probability in the Engineering and Informational Sciences 13: 169–185.Google Scholar
Oluyede, B.O. (2001). On moment inequalities and stochastic ordering for weighted reliability measures. International Journal of Mathematics and Mathematical Sciences 28: 321–330.Google Scholar
Patil, G.P. & Rao, C.R. (1978). Weighted distributions and size-biased sampling with applications to wildlife and human families. Biometrics 34: 179–189.Google Scholar
Zelen, M. & Feinleib, M. (1969). On the theory of screening for chronic diseases. Biometrika 56: 601–614.Google Scholar