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Some inequalities on variances

Published online by Cambridge University Press:  14 July 2016

Matthew Goldstein
Matthew Goldstein*
Affiliation:
Polytechnic Institute of Brooklyn
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Abstract

Sharp upper and lower bounds for the variance of a non-negative function of a non-negative random variable are obtained under rather weak hypotheses regarding the function. Comparisons between bounds are made and some specific examples are considered.

Keywords

VARIANCEINEQUALITYUPPER AND LOWER BOUNDSECONOMIC RISK ANALYSIS
Type
Short Communications
Information
Journal of Applied Probability , Volume 11 , Issue 2 , June 1974 , pp. 409 - 412
Copyright
Copyright © Applied Probability Trust 1974 

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References

[1] Agnew, R. A. (1972) Inequalities with applications in economic risk analysis. J. Appl. Prob. 9, 441–444.Google Scholar
[2] Brook, D. (1966) Bounds for moment generating functions and for extinction probabilities. J. Appl. Prob. 3, 171–178.CrossRefGoogle Scholar