On the maximum entropy distributions of inherently positive nuclear data

• Published in: Nuclear instruments & methods in physics research. Section A, Accelerators, spectrometers, detectors and associated equipment Accelerators, spectrometers, detectors and associated equipment, 2017-05, Vol.854, p.156-162
• Main Authors: Taavitsainen, A., Vanhanen, R.
• Format: Article
• Language: English
• Subjects: Log-normal multivariate distribution; Maximum entropy principle; Normal multivariate distribution; Nuclear data; Truncated multivariate normal distribution; Uncertainty propagation
• ISSN: 0168-9002; 1872-9576
• DOI: 10.1016/j.nima.2016.11.061

The multivariate log-normal distribution is used by many authors and statistical uncertainty propagation programs for inherently positive quantities. Sometimes it is claimed that the log-normal distribution results from the maximum entropy principle, if only means, covariances and inherent positiveness of quantities are known or assumed to be known. In this article we show that this is not true. Assuming a constant prior distribution, the maximum entropy distribution is in fact a truncated multivariate normal distribution – whenever it exists. However, its practical application to multidimensional cases is hindered by lack of a method to compute its location and scale parameters from means and covariances. Therefore, regardless of its theoretical disadvantage, use of other distributions seems to be a practical necessity. •Statistical uncertainty propagation requires a sampling distribution.•The objective distribution of inherently positive quantities is determined.•The objectivity is based on the maximum entropy principle.•The maximum entropy distribution is the truncated normal distribution.•Applicability of log-normal or normal distribution approximation is limited.