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On the quantiles of the gamma and F distributions

Published online by Cambridge University Press:  14 July 2016

I. W. Saunders  and
P. A. P. Moran
I. W. Saunders
Affiliation:
CSIRO Division of Mathematics and Statistics, Canberra
P. A. P. Moran
Affiliation:
The Australian National University, Canberra
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Abstract

We show, in the context of a neurobiological problem, that ζ a(α)−ζ a(β) increases with a, while ζ a (α)/ζ a (β) decreases with a, where 0 < β < α < 1 and ζ a (α) is the α th quantile of either the gamma distribution with shape parameter a, or a scaled F distribution with parameters 2a and 2m for any m.

Keywords

F DISTRIBUTIONGAMMA DISTRIBUTIONQUANTILESORDERING IN DISPERSION
Type
Short Communications
Information
Journal of Applied Probability , Volume 15 , Issue 2 , June 1978 , pp. 426 - 432
Copyright
Copyright © Applied Probability Trust 1978 

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References

Abramowitz, M. A. and Stegun, I. A. (1965) Handbook of Mathematical Functions. Dover, New York.Google Scholar
Lewis, T. (1978) Dispersive distributions, and the connection between dispersivity and strong unimodality. Submitted for publication.Google Scholar
Saunders, I. W. (1978) Locating bright spots in a point process. Adv. Appl. Prob. 10 (3).CrossRefGoogle Scholar