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Health Phys. 2008 Feb;94(2):188-91. doi: 10.1097/01.HP.0000284892.82897.9f.

Analytical approximation of exact Poisson-lognormal likelihood functions.

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Los Alamos National Laboratory, Los Alamos, NM 87545, USA.


Simple analytical approximations of exact Poisson-lognormal likelihood functions are obtained numerically. The Poisson-lognormal statistical model describes counting measurements with lognormally distributed normalization factors. The analytical expressions for the likelihood function allow maximum likelihood data fitting using nonlinear-least-squares-minimization computer programs. A computer program that converts count data into analytical approximation parameters as described in this note is freely available for downloading from the Los Alamos Bayesian Web site (

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