double
gsl_cdf_tdist_Q (const double x, const double nu)
{
double Q;
double x2 = x * x;
if (nu > 30 && x2 < 10 * nu)
{
double u = cornish_fisher (x, nu);
Q = gsl_cdf_ugaussian_Q (u);
return Q;
}
if (x2 < nu)
{
double u = x2 / nu;
double eps = u / (1 + u);
if (x >= 0)
{
Q = beta_inc_AXPY (-0.5, 0.5, 0.5, nu / 2.0, eps);
}
else
{
Q = beta_inc_AXPY (0.5, 0.5, 0.5, nu / 2.0, eps);
}
}
else
{
double v = nu / (x * x);
double eps = v / (1 + v);
if (x >= 0)
{
Q = beta_inc_AXPY (0.5, 0.0, nu / 2.0, 0.5, eps);
}
else
{
Q = beta_inc_AXPY (-0.5, 1.0, nu / 2.0, 0.5, eps);
}
}
return Q;
}
double
gsl_cdf_fdist_Q (const double x, const double nu1, const double nu2)
{
double Q;
double r = nu2 / nu1;
if (x < r)
{
double u = x / (r + x);
Q = beta_inc_AXPY (-1.0, 1.0, nu1 / 2.0, nu2 / 2.0, u);
}
else
{
double u = r / (r + x);
Q = beta_inc_AXPY (1.0, 0.0, nu2 / 2.0, nu1 / 2.0, u);
}
return Q;
}
double
gsl_cdf_beta_Q (const double x, const double a, const double b)
{
double Q;
if ( x >= 1.0)
{
return 0.0;
}
if ( x <= 0.0 )
{
return 1.0;
}
Q = beta_inc_AXPY (-1.0, 1.0, a, b, x);
return Q;
}
double
gsl_cdf_beta_P (const double x, const double a, const double b)
{
double P;
if (x <= 0.0 )
{
return 0.0;
}
if ( x >= 1.0 )
{
return 1.0;
}
P = beta_inc_AXPY (1.0, 0.0, a, b, x);
return P;
}
