/// Error function erf(x). erf(x) = 2/sqrt(pi) * integral (0 to x) { exp(-t^2) dt }
/// @param x input argument
/// @return erf(x)
double errorFunc(const double& x) throw(Exception)
{
if(x < 0) GPSTK_THROW(Exception("Negative first argument"));
try {
return (x < 0.0 ? -incompGamma(0.5,x*x) : incompGamma(0.5,x*x));
}
catch(Exception& e) { GPSTK_RETHROW(e); }
}
/// Error function erf(x). erf(x) = 2/sqrt(pi) * integral (0 to x) { exp(-t^2) dt }
/// @param double x input argument
/// @return erf(x)
double errorFunc(const double& x) throw(Exception)
{
if(x < 0) {
Exception e("Negative first argument in errorFunc()");
GPSTK_THROW(e);
}
try {
return (x < 0.0 ? -incompGamma(0.5,x*x) : incompGamma(0.5,x*x));
}
catch(Exception& e) {
e.addText("Called by errorFunc()");
GPSTK_RETHROW(e);
}
}
/// Cumulative distribution function (CDF) of the Chi-square-distribution.
/// Ref http://www.itl.nist.gov/div898/handbook/ 1.3.6.6.6
/// @param x input statistic value, the RSS of variances, X >= 0
/// @param n degrees of freedom of sample, n > 0
/// @return probability that the sample variance is less than X.
double ChisqCDF(const double& x, const int& n) throw(Exception)
{
if(x < 0) GPSTK_THROW(Exception("Negative statistic"));
if(n <= 0)
GPSTK_THROW(Exception("Non-positive degrees of freedom"));
try {
// NB this incompGamma(n/2,x/2) == NIST's incompGamma(n/2,x/2)/Gamma(n/2)
return incompGamma(double(n)/2.0,x/2.0);
}
catch(Exception& e) { GPSTK_RETHROW(e); }
}
/// Chi-square probability function. ChisqProbability(xsq,n) is defined as the
/// probability that the observed chi-squared for a correct model with n degrees
/// of freedom should be less than the value xsq.
/// @param double xsq input value for chi-squared, xsq > 0
/// @param int n input value for number of degrees of freedom, n > 0
/// @return Chi-squared probability (xsq,n)
double ChisqProbability(const double& x, const int& n) throw(Exception)
{
if(x <= 0) {
Exception e("Non-positive chi-sq argument in ChisqProbability()");
GPSTK_THROW(e);
}
if(n < 0) {
Exception e("Non-positive degrees of freedom in ChisqProbability()");
GPSTK_THROW(e);
}
return incompGamma(double(n)/2.0,x/2.0);
}
