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On Mill's Ratio

Published online by Cambridge University Press:  24 October 2008

Baikunth N. Gupta
Baikunth N. Gupta
Affiliation:
University of Queensland
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Abstract

The inequalities related to Mill's Ratio were conjectured true by Birnbaum (2) and were proved by Murty (4) for sufficiently large x > 0. In the present paper, these are proved for all finite x and have been used to calculate an upper limit for Mill's Ratio over the range x > – 1.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 67 , Issue 2 , March 1970 , pp. 363 - 364
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

(1)Birnbaum, Z. W.An inequality for Mill's Ratio. Ann. Math. Statist. 13 (1942), 245–246.Google Scholar
(2)Birnbaum, Z. W.Effect of linear truncation on a multinormal population. Ann. Math. Statist. 21 (1950), 272–279.CrossRefGoogle Scholar
(3)Gordon, R. D.Values of Mill's Ratio of area to bounding ordinates of the normal probability integral for large values of the argument. Ann. Math. Statist. 12 (1941), 364–366CrossRefGoogle Scholar
(4)Murty, V. N.On a result of Birubaum regarding the skewness of X in a Bivariate normal population. J. Indian Soc. Agric. Statist. 4 (1952), 85–87.Google Scholar