Abstract
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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Dvoretzky, J. Kiefer, and J. Wolfowitz, “Sequential decision problems for processes with continuous time parameter. Testing hypotheses,”Ann. Math. Statist.,27 (1953).
B. V. Gnedenko, ed.,Problems of Reliability Theory [in Russian], Radio i Svyaz, Moscow (1983).
J. G. Kemeny and J. L. Snell,Finite Markov Chains, Van Nostrand, Princeton (1960).
A. M. Kagan, Yu. V. Linnik, and S. R. Rao,Characterization Problems in Mathematical Statistics, Wiley, New York (1973).
Reliability and Effectiveness in Engineering: Experimental Testing, Vol. 6. (Reference Book) [in Russian], Mashinostroenie, Moscow (1986).
S. I. Frolov and V. V. Chichagov, “On calculating the exact value of Kolmogorov's statistic,” in:Nonparametric and Robust Statistical Methods in Cybernetics and Informatics. Vol. 2 [in Russian], Tomsk (1990).
Author information
Authors and Affiliations
Additional information
Translated fromStatisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 186–194, Perm, 1993.
Rights and permissions
About this article
Cite this article
Chichagov, V.V. On some applications of Poisson random walk plans. J Math Sci 81, 2874–2879 (1996). https://doi.org/10.1007/BF02362495
Issue Date:
DOI: https://doi.org/10.1007/BF02362495