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.
"Estimates of Bounded Relative Error in Particle Counting." Ann. Math. Statist. 26 (2) 276 - 285, June, 1955. https://doi.org/10.1214/aoms/1177728544