float8 studentT_cdf(int64 nu, float8 t) {
float8 z,
t_by_sqrt_nu;
float8 A, /* contains A(t|nu) */
prod = 1.,
sum = 1.;
/* Handle extreme cases. See above. */
if (nu <= 0)
return NAN;
else if (nu >= 1000000)
return normal_cdf(t);
else if (nu >= 200)
return studentT_cdf_approx(nu, t);
/* Handle main case (nu < 200) in the rest of the function. */
z = 1. + t * t / nu;
t_by_sqrt_nu = fabs(t) / sqrt(nu);
if (nu == 1)
{
A = 2. / M_PI * atan(t_by_sqrt_nu);
}
else if (nu & 1) /* odd nu > 1 */
{
for (int j = 2; j <= nu - 3; j += 2)
{
prod = prod * j / ((j + 1) * z);
sum = sum + prod;
}
A = 2 / M_PI * ( atan(t_by_sqrt_nu) + t_by_sqrt_nu / z * sum );
}
else /* even nu */
{
for (int j = 2; j <= nu - 2; j += 2)
{
prod = prod * (j - 1) / (j * z);
sum = sum + prod;
}
A = t_by_sqrt_nu / sqrt(z) * sum;
}
/* A should obviously lie withing the interval [0,1] plus minus (hopefully
* small) rounding errors. */
if (A > 1.)
A = 1.;
else if (A < 0.)
A = 0.;
/* The Student-T distribution is obviously symmetric around t=0... */
if (t < 0)
return .5 * (1. - A);
else
return 1. - .5 * (1. - A);
}
double studentT_CDF(int64_t nu, double t) {
double z,
t_by_sqrt_nu;
double A, /* contains A(t|nu) */
prod = 1.,
sum = 1.;
/* Handle extreme cases. See above. */
if (nu <= 0)
return std::numeric_limits<double>::quiet_NaN();
else if (t == std::numeric_limits<double>::infinity())
return 1;
else if (t == -std::numeric_limits<double>::infinity())
return 0;
else if (nu >= 1000000)
return normal_cdf(t);
else if (nu >= 200)
return studentT_cdf_approx(nu, t);
/* Handle main case (nu < 200) in the rest of the function. */
z = 1. + t * t / nu;
t_by_sqrt_nu = std::fabs(t) / std::sqrt(static_cast<double>(nu));
if (nu == 1)
{
A = 2. / M_PI * std::atan(t_by_sqrt_nu);
}
else if (nu & 1) /* odd nu > 1 */
{
for (int j = 2; j <= nu - 3; j += 2)
{
prod = prod * j / ((j + 1) * z);
sum = sum + prod;
}
A = 2 / M_PI * ( std::atan(t_by_sqrt_nu) + t_by_sqrt_nu / z * sum );
}
else /* even nu */
{
for (int j = 2; j <= nu - 2; j += 2)
{
prod = prod * (j - 1) / (j * z);
sum = sum + prod;
}
A = t_by_sqrt_nu / std::sqrt(z) * sum;
}
/* A should obviously be within the interval [0,1] plus minus (hopefully
* small) rounding errors. */
if (A > 1.)
A = 1.;
else if (A < 0.)
A = 0.;
/* The Student-T distribution is obviously symmetric around t=0... */
if (t < 0)
return .5 * (1. - A);
else
return 1. - .5 * (1. - A);
}
