[STATISTICS-52] High precision PDF for the Normal distribution

• 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: 17/Jan/22 16:40
• Updated: 06/Dec/22 11:30
• Resolved: 21/Jan/22 15:04

Description

The normal distribution PDF is computed using:

 

Math.exp(-0.5 * x * x) / Math.sqrt(2 * Math.PI)

The value x^2 can be computed to extended precision. This extra information in the round-off bits can increase the accuracy of the exponential function (see NUMBERS-177 under the title 'Accurate scaling by exp(z*z)').

 

The effect of including the round-off bits on both accuracy and speed should be investigated.