[jira] [Issue Comment Edited] (MATH-364) Make Erf more precise in the tails by providing erfc

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[jira] [Issue Comment Edited] (MATH-364) Make Erf more precise in the tails by providing erfc

ASF GitHub Bot (Jira)

    [ https://issues.apache.org/jira/browse/MATH-364?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13091805#comment-13091805 ]

Christian Winter edited comment on MATH-364 at 8/26/11 2:58 PM:
----------------------------------------------------------------

I added a file here which implements the solution for Erf.erf(double, double), an according JUnit test, and the solution for NormalDistributionImpl.cumulativeDistribution(double, double)

      was (Author: cwinter):
    Implementation of the solutions to Math-364
 

> Make Erf more precise in the tails by providing erfc
> ----------------------------------------------------
>
>                 Key: MATH-364
>                 URL: https://issues.apache.org/jira/browse/MATH-364
>             Project: Commons Math
>          Issue Type: Improvement
>    Affects Versions: 1.1, 1.2, 2.0, 2.1
>            Reporter: Christian Winter
>            Priority: Minor
>             Fix For: 3.0
>
>         Attachments: Math-364_patch.patch
>
>
> First I want to thank Phil Steitz for making Erf stable in the tails through adjusting the choices in calculating the regularized gamma functions, see [Math-282|https://issues.apache.org/jira/browse/MATH-282]. However, the precision of Erf in the tails is limitted to fixed point precision because of the closeness to +/-1.0, although the Gamma class could provide much more accuracy. Thus I propose to add the methods erfc(double) and erf(double, double) to the class Erf:
> {code:borderStyle=solid}
> /**
>  * Returns the complementary error function erfc(x).
>  * @param x the value
>  * @return the complementary error function erfc(x)
>  * @throws MathException if the algorithm fails to converge
>  */
> public static double erfc(double x) throws MathException {
> double ret = Gamma.regularizedGammaQ(0.5, x * x, 1.0e-15, 10000);
> if (x < 0) {
> ret = -ret;
> }
> return ret;
> }
> /**
>  * Returns the difference of the error function values of x1 and x2.
>  * @param x1 the first bound
>  * @param x2 the second bound
>  * @return erf(x2) - erf(x1)
>  * @throws MathException
>  */
> public static double erf(double x1, double x2) throws MathException {
> if(x1>x2)
> return erf(x2, x1);
> if(x1==x2)
> return 0.0;
>    
> double f1 = erf(x1);
> double f2 = erf(x2);
>
> if(f2 > 0.5)
> if(f1 > 0.5)
> return erfc(x1) - erfc(x2);
> else
> return (0.5-erfc(x2)) + (0.5-f1);
> else
> if(f1 < -0.5)
> if(f2 < -0.5)
> return erfc(-x2) - erfc(-x1);
> else
> return (0.5-erfc(-x1)) + (0.5+f2);
> else
> return f2 - f1;
> }
> {code}
> Further this can be used to improve the NormalDistributionImpl through
> {code:borderStyle=solid}
> @Override
> public double cumulativeProbability(double x0, double x1) throws MathException {
> return 0.5 * Erf.erf(
> (x0 - getMean()) / (getStandardDeviation() * sqrt2),
> (x1 - getMean()) / (getStandardDeviation() * sqrt2) );
> }
> {code}

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