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A dam with inverse Gaussian input

Published online by Cambridge University Press:  24 October 2008

A. M. Hasofer
A. M. Hasofer
Affiliation:
University of Tasmania
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Extract

Gani and Prabhu (1) have presented a general theory of storage for dams subject to a steady release. At time t ≥ 0, let a dam of infinite capacity have a continuous random content Z(t) ≥ 0; the input X(t) ≥ 0 which has entered it during time t follows an infinitely divisible distribution, while the dam is subject to a steady release at constant unit rate except if it is empty, when the release ceases. A procedure is obtained whereby various functions describing the transient behaviour of Z(t) can be calculated in principle.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 60 , Issue 4 , October 1964 , pp. 931 - 933
Copyright
Copyright © Cambridge Philosophical Society 1964

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References

REFERENCES

(1)Gani, J. and Prabhu, N. U.A storage model with continuous infinitely divisible inputs. Proc. Cambridge Philos. Soc. 59 (1963), 417–430.CrossRefGoogle Scholar
(2)Kendall, D. G.Some problems in the theory of dams. J. Roy. Statist. Soc. Ser. B, 19 (1957), 207–212.Google Scholar
(3)Lloyd, E. H.The epochs of emptiness of a semi-infinite discrete reservoir. J. Roy. Statist. Soc. Ser. B, 25 (1963), 131–136.Google Scholar
(4)Moran, P. A. P.A probability theory of a dam with a continuous release. Quart. J. Math. Oxford Ser. 2, 7 (1956), 130–137.CrossRefGoogle Scholar
(5)Tweedie, M. C. K.Statistical properties of Inverse Gaussian Distributions. I. Ann. Math. Statist. 28 (1957), 362–377.CrossRefGoogle Scholar