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June, 1955 Estimates of Bounded Relative Error in Particle Counting
M. A. Girshick, H. Rubin, R. Sitgreaves
Ann. Math. Statist. 26(2): 276-285 (June, 1955). DOI: 10.1214/aoms/1177728544


A statistical problem arising in many fields of activity requires the estimation of the average number of events occurring per unit of a continuous variable, such as area or time. The underlying distribution of events is assumed to be Poisson; the constant to be estimated is the unknown parameter $\lambda$ of the distribution. A sampling procedure is proposed in which the continuous variable is observed until a fixed number $M$ of events occurs. Such a procedure enables us to form an estimate $l$, which with confidence coefficient $\alpha$ does not differ from $\lambda$ by more than 100 $\gamma$ per cent of $\lambda$. The values of $\gamma$ and $\alpha$ depend on $M$ but not on $\lambda$. Modifications of this procedure which are sequential in nature and have possible operational advantages are also described. These procedures are discussed in terms of a chemical problem of particle counting. It is clear, however, that they are generally applicable whenever the basic probability assumptions apply.


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M. A. Girshick. H. Rubin. R. Sitgreaves. "Estimates of Bounded Relative Error in Particle Counting." Ann. Math. Statist. 26 (2) 276 - 285, June, 1955.


Published: June, 1955
First available in Project Euclid: 28 April 2007

zbMATH: 0068.13103
MathSciNet: MR69454
Digital Object Identifier: 10.1214/aoms/1177728544

Rights: Copyright © 1955 Institute of Mathematical Statistics

Vol.26 • No. 2 • June, 1955
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