On some applications of Poisson random walk plans

In the present paper, we consider sequential Poisson random walk plans (SPRWPs). In particular, we solve such problems as the calculation of characteristics of SPRWPs with intensity parameter given, the construction of unbiased estimates of characteristics of a homogeneous Poisson process observed in the case of a sequential trial plan, the construction of the joint distribution of Smirnov statistics, and the derivation of an optimal sequential Poisson criterion of given power. Another form of representing exact formulas for calculating characteristics of SPRWPs was given by A. Dvoretsky, J. Kiefer, and J. Wolfowitz. But they note no relationship between the SPRWPs and the corresponding sequential criteria; hence those formulas became approximate but not exact for the sequential criteria. Translated fromStatisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 186–194, Perm, 1993.