Stopping times of one-sample rank order sequential probability ratio tests (Q1059353)

Let \(Z_ 1,Z_ 2,..\). be a sequence of i.i.d. random variables having a continuous d.f. F(x). Assume that the Z's are observed sequentially one at a time. The stopping time T of one-sample rank order sequential probability ratio tests, proposed by \textit{H. D. Weed, R. A. Bradley} and the author [Ann. Stat. 2, 1314-1322 (1974; Zbl 0308.62078)], for the symmetry of F(x) under Lehmann alternatives is investigated. It is shown that if a certain random variable U(Z) is not identically zero then the stopping time T of the sequential procedure is finite with probability one and the moment generating function of T exists.