[STATISTICS-46] TruncatedNormalDistribution

• Type: Improvement
• Status: Closed
• Priority: Minor
• Resolution: Implemented
• Affects Version/s: 1.0
• Fix Version/s: 1.0
• Component/s: distribution
• Assignee: Unassigned
• Reporter: Alex Herbert
• Created: 22/Oct/21 13:52
• Updated: 06/Dec/22 11:30
• Resolved: 11/Dec/21 08:47

Description

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:

mean=7.1, sd=9.9, a=7.0999999, b=7.1000001

The implementation should be improved. I found one method based on the paper:

Foulley JL. A completion simulator for the two-sided truncated
normal distribution. Genetics, selection, evolution 2000
Nov-Dec;32(6): p. 631-635.

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.