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Bounds on the distance of a mixture from its parent distribution

Published online by Cambridge University Press:  14 July 2016

Moshe Shaked
Moshe Shaked*
Affiliation:
Indiana University
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Abstract

In a series of recent papers, Heyde (1975), Heyde and Leslie (1976), Hall (1979) and Brown (1980) obtained upper bounds on the uniform distance of a scale mixture from its parent distribution. Using a different technique we obtain further bounds which are more meaningful and superior in some applications. The new technique is then applied to obtain bounds on the uniform distance of a location mixture from its parent distribution. Comparison of the new bounds and the earlier ones is given.

Keywords

SCALE MIXTURESDISTANCEUNIFORM DISTANCELOCATION MIXTURESRELIABILITY THEORYHAZARD RATE
Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 4 , December 1981 , pp. 853 - 863
Copyright
Copyright © Applied Probability Trust 1981 

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References

Brown, M. (1980) Approximating DFR distributions by exponential distributions, with applications to first passage times. Anh. Prob. To appear.Google Scholar
Hall, P. (1979) On measures of the distance of a mixture from its parent distribution. Stoch. Proc. Appl. 8, 357–365.CrossRefGoogle Scholar
Heyde, C. C. (1975) Kurtosis and departure from normality. In Statistical Distributions in Scientific Work , ed. Patil, G. P., Kotz, S. and Ord, J. K., Reidel, Dordrecht, 193–201.Google Scholar
Heyde, C. C. and Leslie, J. R. (1976) On moment measures of departure from normal and exponential laws. Stoch. Proc. Appl. 4, 317–328.Google Scholar
Karlin, S. (1968) Total Positivity. Stanford University Press, Stanford.Google Scholar
Keilson, J. and Steutel, F. W. (1974) Mixtures of distributions, moment inequalities and measures of exponentiality and normality. Ann. Prob. 2, 112–130.CrossRefGoogle Scholar
Shaked, M. (1977) Statistical inference for a class of life distributions. Comm. Statist. Theory. Methods A6, 1323–1339.Google Scholar
Shaked, M. (1978) Accelerated life testing for a class of linear hazard rate type distributions. Technometrics 20, 457–466.CrossRefGoogle Scholar