Europhys. Lett.
Volume 67, Number 4, August 2004
Page(s) 572 - 578
Section General
Published online 01 August 2004
Europhys. Lett., 67 (4), pp. 572-578 (2004)
DOI: 10.1209/epl/i2004-10097-5

Quantum test of the distributions of composite physical measurements

M. P. Silverman1, W. Strange1 and T. C. Lipscombe2

1  Department of Physics, Trinity College - Hartford, CT 06106, USA
2  Johns Hopkins University - Baltimore, MD 21218, USA

(Received 5 January 2004; accepted in final form 4 June 2004)

Probability distribution functions and lowest statistical moments of composite measurements representable as products and quotients of independent normal variates are derived, and tested by means of the $\alpha$ and $\beta$ branching decays of $\chem{{}^{212}Bi}$. The exact composite distribution functions are non-Gaussian and provide correct uncertainty estimates and confidence intervals in cases where standard error propagation relations are inaccurate. Although nuclear decay processes give rise to Poisson-distributed parent populations, the Gaussian-based composite distributions form nearly perfect envelopes to the discrete distributions of products and ratios of Poisson variates, even for relatively low counts. To our knowledge, this is the first reported experimental test of the statistics of composite measurements by a fundamental quantum process.

06.20.Dk - Measurement and error theory.
81.70.-q - Methods of materials testing and analysis.

© EDP Sciences 2004