public static double qnbeta(
double p, double a, double b, double ncp, boolean lower_tail, boolean log_p) {
final double accu = 1e-15;
final double Eps = 1e-14; /* must be > accu */
double ux, lx, nx, pp;
if (DoubleVector.isNaN(p)
|| DoubleVector.isNaN(a)
|| DoubleVector.isNaN(b)
|| DoubleVector.isNaN(ncp)) {
return p + a + b + ncp;
}
if (!DoubleVector.isFinite(a)) {
return DoubleVector.NaN;
}
if (ncp < 0. || a <= 0. || b <= 0.) {
return DoubleVector.NaN;
}
// R_Q_P01_boundaries(p, 0, 1);
if ((log_p && p > 0) || (!log_p && (p < 0 || p > 1))) {
return DoubleVector.NaN;
}
if (p == SignRank.R_DT_0(lower_tail, log_p)) {
return 0.0;
}
if (p == SignRank.R_DT_1(lower_tail, log_p)) {
return 1.0;
}
// end of R_Q_P01_boundaries
p = Normal.R_DT_qIv(p, log_p ? 1.0 : 0.0, lower_tail ? 1.0 : 0.0);
/* Invert pnbeta(.) :
* 1. finding an upper and lower bound */
if (p > 1 - SignRank.DBL_EPSILON) {
return 1.0;
}
pp = Math.min(1 - SignRank.DBL_EPSILON, p * (1 + Eps));
for (ux = 0.5;
ux < 1 - SignRank.DBL_EPSILON && pnbeta(ux, a, b, ncp, true, false) < pp;
ux = 0.5 * (1 + ux)) ;
pp = p * (1 - Eps);
for (lx = 0.5; lx > Double.MIN_VALUE && pnbeta(lx, a, b, ncp, true, false) > pp; lx *= 0.5) ;
/* 2. interval (lx,ux) halving : */
do {
nx = 0.5 * (lx + ux);
if (pnbeta(nx, a, b, ncp, true, false) > p) {
ux = nx;
} else {
lx = nx;
}
} while ((ux - lx) / nx > accu);
return 0.5 * (ux + lx);
}
@Primitive
public static double pnbeta(
double x, double a, double b, double ncp, boolean lower_tail, boolean log_p) {
if (DoubleVector.isNaN(x)
|| DoubleVector.isNaN(a)
|| DoubleVector.isNaN(b)
|| DoubleVector.isNaN(ncp)) {
return x + a + b + ncp;
}
// R_P_bounds_01(x, 0., 1.);
if (x <= 0.0) {
return SignRank.R_DT_0(lower_tail, log_p);
}
if (x >= 1.0) {
return SignRank.R_DT_1(lower_tail, log_p);
}
return pnbeta2(x, 1 - x, a, b, ncp, lower_tail, log_p);
}