American Institute of Mathematical Sciences

Advanced
2008, 5(4): 647-667. doi: 10.3934/mbe.2008.5.647

Quantifying uncertainty in the estimation of probability distributions

H.T. Banks 1, and  Jimena L. Davis 1,

1. 

Center for Research in Scientific Computation, North Carolina State University, Raleigh, North Carolina 27695-8205, United States

Received  December 2007 Revised  March 2008 Published  October 2008

We consider ordinary least squares parameter estimation problems where the unknown parameters to be estimated are probability distributions. A computational framework for quantification of uncertainty (e.g., standard errors) associated with the estimated parameters is given and sample numerical findings are presented.
Keywords: parameter estimation, asymptotic standard error theory, confidence bands, probability distributions, approximation, size-structured populations.
Mathematics Subject Classification: 35L60,62E20,62F25,62G15,65M32,92D25.
Citation: H.T. Banks, Jimena L. Davis. Quantifying uncertainty in the estimation of probability distributions. Mathematical Biosciences & Engineering, 2008, 5 (4) : 647-667. doi: 10.3934/mbe.2008.5.647
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