First Emptiness in a Finite Dam
- 1 July 1961
- journal article
- research article
- Published by Oxford University Press (OUP) in Journal of the Royal Statistical Society Series B: Statistical Methodology
- Vol. 23 (2) , 343-351
- https://doi.org/10.1111/j.2517-6161.1961.tb00416.x
Abstract
SUMMARY: This paper discusses problems of first emptiness in a finite discrete dam (i) before overflow occurs, and (ii) where there is overflowing. Equations for probabilities of first emptiness in both cases are derived, and their generating functions found. The latter are shown to be the ratio of two polynomials. For geometric inputs, explicit expressions for these polynomials may be found similar to Feller’s results for classical random walk.This publication has 3 references indexed in Scilit:
- Some Exact Results for the Finite DamThe Annals of Mathematical Statistics, 1958
- Elementary methods for an occupancy problem of storageMathematische Annalen, 1958
- Some Problems in the Theory of DamsJournal of the Royal Statistical Society Series B: Statistical Methodology, 1957