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);
}
@Primitive
public static double dnbeta(double x, double a, double b, double ncp, boolean give_log) {
final double eps = 1.e-15;
int kMax;
double k, ncp2, dx2, d, D;
double sum, term, p_k, q; /* They were LDOUBLE */
if (DoubleVector.isNaN(x)
|| DoubleVector.isNaN(a)
|| DoubleVector.isNaN(b)
|| DoubleVector.isNaN(ncp)) {
return x + a + b + ncp;
}
if (ncp < 0 || a <= 0 || b <= 0) {
return DoubleVector.NaN;
}
if (!DoubleVector.isFinite(a) || !DoubleVector.isFinite(b) || !DoubleVector.isFinite(ncp)) {
return DoubleVector.NaN;
}
if (x < 0 || x > 1) {
return (SignRank.R_D__0(true, give_log));
}
if (ncp == 0) {
return Distributions.dbeta(x, a, b, give_log);
}
/* New algorithm, starting with *largest* term : */
ncp2 = 0.5 * ncp;
dx2 = ncp2 * x;
d = (dx2 - a - 1) / 2;
D = d * d + dx2 * (a + b) - a;
if (D <= 0) {
kMax = 0;
} else {
D = Math.ceil(d + Math.sqrt(D));
kMax = (D > 0) ? (int) D : 0;
}
/* The starting "middle term" --- first look at it's log scale: */
term = Distributions.dbeta(x, a + kMax, b, /* log = */ true);
p_k = Poisson.dpois_raw(kMax, ncp2, true);
if (x == 0.
|| !DoubleVector.isFinite(term)
|| !DoubleVector.isFinite(p_k)) /* if term = +Inf */ {
return SignRank.R_D_exp(p_k + term, true, give_log);
}
/* Now if s_k := p_k * t_k {here = exp(p_k + term)} would underflow,
* we should rather scale everything and re-scale at the end:*/
p_k += term; /* = log(p_k) + log(t_k) == log(s_k) -- used at end to rescale */
/* mid = 1 = the rescaled value, instead of mid = exp(p_k); */
/* Now sum from the inside out */
sum = term = 1. /* = mid term */;
/* middle to the left */
k = kMax;
while (k > 0 && term > sum * eps) {
k--;
q = /* 1 / r_k = */ (k + 1) * (k + a) / (k + a + b) / dx2;
term *= q;
sum += term;
}
/* middle to the right */
term = 1.;
k = kMax;
do {
q = /* r_{old k} = */ dx2 * (k + a + b) / (k + a) / (k + 1);
k++;
term *= q;
sum += term;
} while (term > sum * eps);
return SignRank.R_D_exp(p_k + Math.log(sum), true, give_log);
}