Science China Mathematics

, Volume 53, Issue 4, pp 917–926 | Cite as

Method of sequential mesh on Koopman-Darmois distributions

  • Yan Li
  • XiaoLong Pu


For costly and/or destructive tests, the sequential method with a proper maximum sample size is needed. Based on Koopman-Darmois distributions, this paper proposes the method of sequential mesh, which has an acceptable maximum sample size. In comparison with the popular truncated sequential probability ratio test, our method has the advantage of a smaller maximum sample size and is especially applicable for costly and/or destructive tests.


method of sequential mesh sequential probability ratio test (SPRT) Koopman-Darmois distributions maximum sample size 


62F03 62L05 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Anderson T W. A modification of the sequential probability ratio test to reduce the sample size. Ann Math Statist, 1960, 31: 165–197zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bilias Y. Sequential testing of duration data: the case of the pennsylvania “reemployment bonus” experiment. J Appl Econometrics, 2000, 15: 575–594CrossRefGoogle Scholar
  3. 3.
    Donnelly T G. A family of truncated sequential tests. Dissertation for the Doctoral Degree. NC: University of North Carolina, 1957Google Scholar
  4. 4.
    Huffman M D. An efficient approximate solution to the Kiefer-Weiss problem. Ann Statist, 1983, 11: 306–316zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Ingeborg T, Paulus A H N. Early stopping in clinical trials and epidemiologic studies for “futility”: conditional power versus sequential analysis. J Clinical Epidemiology, 2003, 56: 610–617CrossRefGoogle Scholar
  6. 6.
    International Electrotechnical Commission. International Standard of IEC 1123: Reliability testing compliance test plans for success ratio, 1991–12Google Scholar
  7. 7.
    Kiefer J, Weiss L. Some properties of generalized sequential probability ratio tests. Ann Math Statist, 1957, 28: 57–75zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Lai T L. Optimal stopping and sequential tests which minimize the maximum expected sample size. Ann Statist, 1973, 1: 659–673zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Lai T L. Sequential analysis: some classical problems and new challenges. Statist Sinica, 2001, 11: 303–408zbMATHMathSciNetGoogle Scholar
  10. 10.
    Lorden G. 2-SPRT’s and the modified Kiefer-Weiss problem of minimizing an expected sample size. Ann Math Statist, 1976, 4: 281–291zbMATHMathSciNetGoogle Scholar
  11. 11.
    Marano S, Willett P, Matta V. Sequential testing of sorted and transformed data as an efficient way to implement long GLRTs. IEEE Trans Signal Process, 2003, 51: 325–337CrossRefMathSciNetGoogle Scholar
  12. 12.
    Pu X L, Yan Z G, Mao S S, et al. The sequential mesh test for a proportion (in Chinese). J East China Norm Univ Natur Sci Ed, 2006, 1: 63–71MathSciNetGoogle Scholar
  13. 13.
    Wald A. Sequential Analysis. New York: Wiley, 1947zbMATHGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.School of Finance and StatisticsEast China Normal UniversityShanghaiChina

Personalised recommendations