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An Inequality Satisfied by the Gamma Function

Published online by Cambridge University Press:  20 November 2018

J. B. Selliah
J. B. Selliah*
Affiliation:
University of Toronto, Toronto, Ontario
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Gurland [1] by making use of the Cramer-Rao lower bound for the variance of an unbiased estimator obtained the following inequality

1

for real values of α and δ satisfying α+δ>0, α≠0, δ>0. He used the fact that (Γ(δ)Γ(δ+α))xα is an unbiased estimator of θα where θ is the parameter for the density function

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 19 , Issue 1 , 01 March 1976 , pp. 85 - 87
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Gurland, J., An inequality satisfied by the Gamma Function, Skand Akt. (1956), 171–172.Google Scholar
2. Olkin, I., An inequality satisfied by the Gamma Function, Skand Akt. (1958), 37–39.Google Scholar