The paper addresses the sequential sampling issues related to attainment of a given number of events in a Poisson process. The problem of guaranteeing the necessary sample size is formulated as that of open-ended hypothesis testing in which one has to find a one-sided stopping boundary. The formulas for the distribution of general stopping times are derived, and for the linear boundary they are shown to be in the class of Lagrangian Poisson distributions. A locally optimal testing procedure is obtained.
Citation: Communications in Statistics Part A-Theory and Methods
Pub Type: Journals
Borel distribution, Lagrangian Poisson distribution, locally optimal test, one-sided stopping boundary, Poisson process.