Alex Herbert created STATISTICS-46:
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Summary: 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
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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