Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 393095, 15 pages
Research Article

Hypothesis Designs for Three-Hypothesis Test Problems

School of Finance and Statistics, East China Normal University, No. 500 Dongchuan Road, Shanghai 200241, China

Received 25 January 2010; Accepted 18 March 2010

Academic Editor: Ming Li

Copyright © 2010 Yan Li and Xiaolong Pu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


As a helpful guide for applications, the alternative hypotheses of the three-hypothesis test problems are designed under the required error probabilities and average sample number in this paper. The asymptotic formulas and the proposed numerical quadrature formulas are adopted, respectively, to obtain the hypothesis designs and the corresponding sequential test schemes under the Koopman-Darmois distributions. The example of the normal mean test shows that our methods are quite efficient and satisfactory for practical uses.