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On an inequality for the normal distribution arising in bioequivalence studies

Published online by Cambridge University Press:  14 July 2016

Yi-Ching Yao*
Affiliation:
Academia Sinica
Hari Iyer*
Affiliation:
Colorado State University
*
Postal address: Institute of Statistical Science, Academia Sinica, Taipei, Taiwan, R.O.C. Email address: yao@stat.sinica.edu.tw
∗∗Postal address: Department of Statistics, Colorado State University, Fort Collins, CO 80523, USA.

Abstract

For (μ,σ2) ≠ (0,1), and 0 < z < ∞, we prove that where φ and Φ are, respectively, the p.d.f. and the c.d.f. of a standard normal random variable. This inequality is sharp in the sense that the right-hand side cannot be replaced by a larger quantity which depends only on μ and σ. In other words, for any given (μ,σ) ≠ (0,1), the infimum, over 0 < z < ∞, of the left-hand side of the inequality is equal to the right-hand side. We also point out how this inequality arises in the context of defining individual bioequivalence.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 1999 

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References

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