commons-issues mailing list archives

Site index · List index
Message view
Top
From "Christian Winter (JIRA)" <j...@apache.org>
Subject [jira] Created: (MATH-364) Make Erf more precise in the tails by providing erfc
Date Tue, 13 Apr 2010 08:14:49 GMT
```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: 2.1
Reporter: Christian Winter
Priority: Minor

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}

--
This message is automatically generated by JIRA.
-
If you think it was sent incorrectly contact one of the administrators: https://issues.apache.org/jira/secure/Administrators.jspa
-