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https://issues.apache.org/jira/browse/STATISTICS-46?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
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Alex Herbert resolved STATISTICS-46.
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Fix Version/s: 1.0
Resolution: Implemented
Added in commit:
62829a20efe3dfd2123ab4227c6c4ec109cd85eb
> TruncatedNormalDistribution
> ---------------------------
>
> Key: STATISTICS-46
> URL: https://issues.apache.org/jira/browse/STATISTICS-46
> Project: Apache Commons Statistics
> Issue Type: Improvement
> Components: distribution
> Affects Versions: 1.0
> Reporter: Alex Herbert
> Priority: Minor
> Fix For: 1.0
>
> Attachments: erf_minus_x_derf_dx.png
>
>
> The TruncatedNormalDistribution computes the moments using the formulas on
> the Wikipedia page:
> [https://en.wikipedia.org/wiki/Truncated_normal_distribution#Moments]
> For the two sided truncation this computation is unstable. This is noted for
> the case when the bound [a, b] is far from the mean. It also effects a
> current test case for the following:
> {noformat}
> mean=7.1, sd=9.9, a=7.0999999, b=7.1000001
> {noformat}
> The implementation should be improved. I found one method based on the paper:
> {noformat}
> Foulley JL. A completion simulator for the two-sided truncated
> normal distribution. Genetics, selection, evolution 2000
> Nov-Dec;32(6): p. 631-635.
> {noformat}
> When the bound [a, b] is far from the mean the range is in the long flat tail
> of the normal distribution. Here the moments can be computed as if the
> distribution is a continuous uniform distribution.
> Note that the mean and variance are not used by the implementation. Improving
> the computation will simply provide a better result if the moments are
> desired.
>
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