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On the conditional expected value of contributions from a renewal process

Published online by Cambridge University Press:  14 July 2016

M. F. James
M. F. James*
Affiliation:
General Reactor Physics Division, A.E.E., Winfrith, Dorset
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Abstract

The problem discussed in this paper arose from the study of the effects of unresolved resonances on neutron cross-sections, but it is considered here in more general terms.

Events in a modified renewal process occur at successive intervals x1, x2, …, and the ith event has associated with it a parameter Γi. The random variables xi and Γi are all independent, and their probability distribution functions are known. Each event contributes to two quantities F(u) and G(v) measured at u and v respectively. The value of the total contribution of all events to G(v) is assumed to be known from observation: this paper gives formulae for the mean value of F(u) conditional on this known value of G(v).

Type
Research Papers
Information
Journal of Applied Probability , Volume 3 , Issue 2 , December 1966 , pp. 464 - 480
Copyright
Copyright © Applied Probability Trust 

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References

6. References

Cox, D. R. (1962) Renewal Theory, Methuen, London.Google Scholar
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Hammersley, J. M. (1958) Discussion on Dr. Smith's paper. J. R. Statist. Soc. B20, 287–289.Google Scholar
Reichel, A. and Wilkins, C. A. (1964) On the theory of resonance integrals in the statistical region. J. Appl. Prob. 1, 335–346.Google Scholar