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A class of distribution function processes which have derivatives

Published online by Cambridge University Press:  14 July 2016

Charles H. Kraft
Charles H. Kraft*
Affiliation:
University of Minnesota
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Extract

In the .author and van Eeden considered, as prior distributions for the cumulative, F, of the bio-assay problem, processes whose sample functions are, with probability one, distribution functions. The example we considered there had the undesirable property that its mean, E(F), was singular with respect to Lebesgue measure. In fact, Dubins and Freedman have shown that a class of such processes, which includes the example we considered, has sample functions F which are, with probability one, singular.

Type
Short Communications
Information
Journal of Applied Probability , Volume 1 , Issue 2 , December 1964 , pp. 385 - 388
Copyright
Copyright © Applied Probability Trust 

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References

[1] Kraft, Charles H. and Eeden, Constance Van (1964) Bayesian bio-assay. Note to appear in Ann. Math. Statist. CrossRefGoogle Scholar
[2] Dubins, L. E. and Freedman, David A. (1963) Random distribution functions. Bull. Amer. Math. Soc. 69, 548–551.CrossRefGoogle Scholar
[3] Doob, J. L. (1953) Stochastic Processes. John Wiley, New York.Google Scholar