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Radiation Protection Dosimetry Advance Access originally published online on January 12, 2007
Radiation Protection Dosimetry 2007 124(2):155-163; doi:10.1093/rpd/ncl544
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Published by Oxford University Press 2007.
The online version of this article has been published under an open access model. Users are entitled to use, reproduce, disseminate, or display the open access version of this article for non-commercial purposes provided that: the original authorship is properly and fully attributed; the Journal and Oxford University Press are attributed as the original place of publication with the correct citation details given; if an article is subsequently reproduced or disseminated not in its entirety but only in part or as a derivative work this must be clearly indicated. For commercial re-use, please contact journals.permissions@oxfordjournals.org.

Statistical modelling of Poisson/log–normal data

Guthrie Miller*

Los Alamos National Laboratory MS-G761 Los Alamos, NM 87545, USA

* Corresponding author: guthrie{at}lanl.gov

Received June 23, 2006, amended November 27, 2006, accepted December 3, 2006

In statistical data fitting, self consistency is checked by examining the closeness of the quantity {chi}2/NDF to 1, where {chi}2 is the sum of squares of data minus fit divided by standard deviation, and NDF is the number of data minus the number of fit parameters. In order to calculate {chi}2 one needs an expression for the standard deviation. In this note several alternative expressions for the standard deviation of data distributed according to a Poisson/log–normal distribution are proposed and evaluated by Monte Carlo simulation. Two preferred alternatives are identified. The use of replicate data to obtain uncertainty is problematic for a small number of replicates. A method to correct this problem is proposed. The log–normal approximation is good for sufficiently positive data. A modification of the log–normal approximation is proposed, which allows it to be used to test the hypothesis that the true value is zero.


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