[
https://issues.apache.org/jira/browse/NUMBERS-169?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
]
Alex Herbert resolved NUMBERS-169.
----------------------------------
Resolution: Won't Do
The complement of the regularized is added in [NUMBERS-181].
> Function to evaluate the complement of the RegularizedBeta
> ----------------------------------------------------------
>
> Key: NUMBERS-169
> URL: https://issues.apache.org/jira/browse/NUMBERS-169
> Project: Commons Numbers
> Issue Type: New Feature
> Components: gamma
> Affects Versions: 1.0
> Reporter: Alex Herbert
> Priority: Major
>
> The RegularizedBeta class computes the regularized beta function I(x, a, b).
> There is a functional identity for this:
> {code:java}
> 1 - I(x, a, b) = I(1 - x, b, a)
> {code}
> See [Wolfram Regularized Incomplete Beta
> Identities|https://functions.wolfram.com/06.21.17.0008.01]
> The RegularizedBeta class currently exploits this identity to compute the
> value by switching to call '1.0 - value(1 - x, b, a)' depending on the
> parameters.
> I suggest a complement for this function to compute 1 - I(x, a, b):
> {code:java}
> public class RegularizedBetac {
> public static double value(double x,
> final double a,
> final double b,
> double epsilon,
> int maxIterations);
> }
> {code}
> This can call RegularizedBeta.value using the same inversion logic and avoid
> a potential computation of the complement using multiple inversions with loss
> of precision:
> {noformat}
> 1 - I(x, a, b) == 1 - [ 1 - I(1 - x, b, a) ] = I(1 - x, b, a)
> or
> I(1 - x, b, a) == 1 - I(x, a, b) = 1 - [ 1 - I(1 - x, b, a) ]
> {noformat}
>
--
This message was sent by Atlassian Jira
(v8.20.1#820001)
