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Journal of Radioanalytical and Nuclear Chemistry

, Volume 314, Issue 2, pp 605–609 | Cite as

Correlation in the application of the triple-to-double coincidence ratio method with unequal photomultiplier tube efficiencies

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Abstract

Counting data from the triple-to-double coincidence ratio (TDCR) method are by their nature highly correlated. In the general case of unequal phototube detection efficiencies, the highly correlated nature of the data combined with the need to apply methods to solve a system of equations makes proper uncertainty analysis difficult. Removing the correlations from the data prior to analysis may assist in this endeavor. This paper describes the de-correlation of TDCR data by the application of a particular linear transform, the Mahalanobis transform. A programming example in MATLAB is given and a practical example of the use of this technique in the analysis of TDCR data is presented.

Keywords

Correlation Liquid scintillation counting Mahalanobis transform Triple-to-double coincidence ratio method 

References

  1. 1.
    Broda R, Cassette P, Kossert K (2007) Radionuclide metrology using liquid scintillation counting. Metrologia 44:36–52CrossRefGoogle Scholar
  2. 2.
    Kossert K, Broda R, Cassette P, Ratel G, Zimmerman BE (2015) Uncertainty determination for activity measurements by means of the TDCR method and the CIEMAT/NIST efficiency tracing technique. Metrologia 52:S172–S190CrossRefGoogle Scholar
  3. 3.
    Kessy A, Lewin A, Strimmer K (2017) Optimal whitening and decorrelation. Am Stat. doi: 10.1080/00031305.2016.1277159 Google Scholar
  4. 4.
    Mahalanobis PC (1936) On the generalized distance in statistics. Proc Natl Inst Sci India 2(1):49–55Google Scholar
  5. 5.
    Vidakovic B (2011) Statistics for bioengineering sciences with MATLAB and WinBUGS support. Springer, BerlinCrossRefGoogle Scholar
  6. 6.
    MATLAB R2016b (2016) MathWorks, NatickGoogle Scholar
  7. 7.
    The R Environment, The R-Foundation (2017) https://www.r-project.org/foundation/. Accessed 25 May 2017
  8. 8.
    Mathematica, Wolfram Research, ChampaignGoogle Scholar
  9. 9.
    Ypma T (1995) The historical development of the Newton–Raphson method. SIAM Rev 37(4):531–551CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2017

Authors and Affiliations

  1. 1.Physical Measurement LaboratoryNational Institute of Standards and TechnologyGaithersburgUSA

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