double qcauchy(double p, double location, double scale,
int lower_tail, int log_p)
{
#ifdef IEEE_754
if (ISNAN(p) || ISNAN(location) || ISNAN(scale))
return p + location + scale;
#endif
R_Q_P01_check(p);
if (scale <= 0 || !R_FINITE(scale)) {
if (scale == 0) return location;
/* else */ ML_ERR_return_NAN;
}
if (log_p) {
if (p > -1) {
/* when ep := exp(p),
* tan(pi*ep)= -tan(pi*(-ep))= -tan(pi*(-ep)+pi) = -tan(pi*(1-ep)) =
* = -tan(pi*(-expm1(p))
* for p ~ 0, exp(p) ~ 1, tan(~0) may be better than tan(~pi).
*/
if (p == 0.) /* needed, since 1/tan(-0) = -Inf for some arch. */
return location + (lower_tail ? scale : -scale) * ML_POSINF;
lower_tail = !lower_tail;
p = -expm1(p);
} else
p = exp(p);
}
return location + (lower_tail ? -scale : scale) / tan(M_PI * p);
/* -1/tan(pi * p) = -cot(pi * p) = tan(pi * (p - 1/2)) */
}
double qpois(double p, double lambda, int lower_tail, int log_p)
{
double mu, sigma, gamma, z, y;
#ifdef IEEE_754
if (ISNAN(p) || ISNAN(lambda))
return p + lambda;
#endif
if(!R_FINITE(lambda))
ML_ERR_return_NAN;
if(lambda < 0) ML_ERR_return_NAN;
R_Q_P01_check(p);
if(lambda == 0) return 0;
if(p == R_DT_0) return 0;
if(p == R_DT_1) return ML_POSINF;
mu = lambda;
sigma = sqrt(lambda);
/* gamma = sigma; PR#8058 should be kurtosis which is mu^-0.5 */
gamma = 1.0/sigma;
/* Note : "same" code in qpois.c, qbinom.c, qnbinom.c --
* FIXME: This is far from optimal [cancellation for p ~= 1, etc]: */
if(!lower_tail || log_p) {
p = R_DT_qIv(p); /* need check again (cancellation!): */
if (p == 0.) return 0;
if (p == 1.) return ML_POSINF;
}
/* temporary hack --- FIXME --- */
if (p + 1.01*DBL_EPSILON >= 1.) return ML_POSINF;
/* y := approx.value (Cornish-Fisher expansion) : */
z = qnorm(p, 0., 1., /*lower_tail*/TRUE, /*log_p*/FALSE);
#ifdef HAVE_NEARBYINT
y = nearbyint(mu + sigma * (z + gamma * (z*z - 1) / 6));
#else
y = round(mu + sigma * (z + gamma * (z*z - 1) / 6));
#endif
z = ppois(y, lambda, /*lower_tail*/TRUE, /*log_p*/FALSE);
/* fuzz to ensure left continuity; 1 - 1e-7 may lose too much : */
p *= 1 - 64*DBL_EPSILON;
/* If the mean is not too large a simple search is OK */
if(lambda < 1e5) return do_search(y, &z, p, lambda, 1);
/* Otherwise be a bit cleverer in the search */
{
double incr = floor(y * 0.001), oldincr;
do {
oldincr = incr;
y = do_search(y, &z, p, lambda, incr);
incr = fmax2(1, floor(incr/100));
} while(oldincr > 1 && incr > lambda*1e-15);
return y;
}
}
double qunif(double p, double a, double b, int lower_tail, int log_p)
{
#ifdef IEEE_754
if (ISNAN(p) || ISNAN(a) || ISNAN(b))
return p + a + b;
#endif
R_Q_P01_check(p);
if (b <= a ) ML_ERR_return_NAN;
return a + R_DT_qIv(p) * (b - a);
}
double qwilcox(double x, double m, double n, int lower_tail, int log_p)
{
double c, p;
#ifdef IEEE_754
if (ISNAN(x) || ISNAN(m) || ISNAN(n))
return(x + m + n);
#endif
if(!R_FINITE(x) || !R_FINITE(m) || !R_FINITE(n))
ML_ERR_return_NAN;
R_Q_P01_check(x);
m = R_forceint(m);
n = R_forceint(n);
if (m <= 0 || n <= 0)
ML_ERR_return_NAN;
if (x == R_DT_0)
return(0);
if (x == R_DT_1)
return(m * n);
if(log_p || !lower_tail)
x = R_DT_qIv(x); /* lower_tail,non-log "p" */
int mm = (int) m, nn = (int) n;
w_init_maybe(mm, nn);
c = choose(m + n, n);
p = 0;
int q = 0;
if (x <= 0.5) {
x = x - 10 * DBL_EPSILON;
for (;;) {
p += cwilcox(q, mm, nn) / c;
if (p >= x)
break;
q++;
}
}
else {
x = 1 - x + 10 * DBL_EPSILON;
for (;;) {
p += cwilcox(q, mm, nn) / c;
if (p > x) {
q = (int) (m * n - q);
break;
}
q++;
}
}
return(q);
}
double qsignrank(double x, double n, int lower_tail, int log_p)
{
double f, p;
#ifdef IEEE_754
if (ISNAN(x) || ISNAN(n))
return(x + n);
#endif
if (!R_FINITE(x) || !R_FINITE(n))
ML_ERR_return_NAN;
R_Q_P01_check(x);
n = floor(n + 0.5);
if (n <= 0)
ML_ERR_return_NAN;
if (x == R_DT_0)
return(0);
if (x == R_DT_1)
return(n * (n + 1) / 2);
if(log_p || !lower_tail)
x = R_DT_qIv(x); /* lower_tail,non-log "p" */
int nn = (int) n;
w_init_maybe(nn);
f = exp(- n * M_LN2);
p = 0;
int q = 0;
if (x <= 0.5) {
x = x - 10 * DBL_EPSILON;
for (;;) {
p += csignrank(q, nn) * f;
if (p >= x)
break;
q++;
}
}
else {
x = 1 - x + 10 * DBL_EPSILON;
for (;;) {
p += csignrank(q, nn) * f;
if (p > x) {
q = (int)(n * (n + 1) / 2 - q);
break;
}
q++;
}
}
return(q);
}
double qcauchy(double p, double location, double scale,
int lower_tail, int log_p)
{
#ifdef IEEE_754
if (ISNAN(p) || ISNAN(location) || ISNAN(scale))
return p + location + scale;
#endif
if(!R_FINITE(p) || !R_FINITE(location) || !R_FINITE(scale))
ML_ERR_return_NAN;
R_Q_P01_check(p);
if (scale <= 0) ML_ERR_return_NAN;
return location + scale * tan(M_PI * (R_DT_qIv(p) - 0.5));
}
double qnchisq(double p, double n, double lambda, int lower_tail, int log_p)
{
const double acu = 1e-12;
const double Eps = 1e-6; /* must be > acu */
double ux, lx, nx;
#ifdef IEEE_754
if (ISNAN(p) || ISNAN(n) || ISNAN(lambda))
return p + n + lambda;
#endif
if (!R_FINITE(n)) ML_ERR_return_NAN;
n = FLOOR(n + 0.5);
if (n < 1 || lambda < 0) ML_ERR_return_NAN;
R_Q_P01_check(p);
if (p == R_DT_0)
return 0;
/* Invert pnchisq(.) finding an upper and lower bound;
then interval halfing : */
p = R_D_qIv(p);
if(lower_tail) {
for(ux = 1.; pnchisq_raw(ux, n, lambda, Eps, 128) < p * (1 + Eps);
ux *= 2){}
for(lx = ux; pnchisq_raw(lx, n, lambda, Eps, 128) > p * (1 - Eps);
lx *= 0.5){}
}
else {
for(ux = 1.; pnchisq_raw(ux, n, lambda, Eps, 128) + p < 1 + Eps;
ux *= 2){}
for(lx = ux; pnchisq_raw(lx, n, lambda, Eps, 128) + p > 1 - Eps;
lx *= 0.5){}
}
p = R_D_Lval(p);
do {
nx = 0.5 * (lx + ux);
if (pnchisq_raw(nx, n, lambda, acu, 1000) > p)
ux = nx;
else
lx = nx;
}
while ((ux - lx) / nx > acu);
return 0.5 * (ux + lx);
}
gnm_float
qcauchy (gnm_float p, gnm_float location, gnm_float scale,
gboolean lower_tail, gboolean log_p)
{
if (gnm_isnan(p) || gnm_isnan(location) || gnm_isnan(scale))
return p + location + scale;
R_Q_P01_check(p);
if (scale < 0 || !gnm_finite(scale)) ML_ERR_return_NAN;
if (log_p) {
if (p > -1)
/* The "0" here is important for the p=0 case: */
lower_tail = !lower_tail, p = 0 - gnm_expm1 (p);
else
p = gnm_exp (p);
}
if (lower_tail) scale = -scale;
return location + scale / gnm_tan(M_PIgnum * p);
}
double igraph_qnorm5(double p, double mu, double sigma, int lower_tail, int log_p)
{
double p_, q, r, val;
#ifdef IEEE_754
if (ISNAN(p) || ISNAN(mu) || ISNAN(sigma))
return p + mu + sigma;
#endif
if (p == R_DT_0) return ML_NEGINF;
if (p == R_DT_1) return ML_POSINF;
R_Q_P01_check(p);
if(sigma < 0) ML_ERR_return_NAN;
if(sigma == 0) return mu;
p_ = R_DT_qIv(p);/* real lower_tail prob. p */
q = p_ - 0.5;
/*-- use AS 241 --- */
/* double ppnd16_(double *p, long *ifault)*/
/* ALGORITHM AS241 APPL. STATIST. (1988) VOL. 37, NO. 3
Produces the normal deviate Z corresponding to a given lower
tail area of P; Z is accurate to about 1 part in 10**16.
(original fortran code used PARAMETER(..) for the coefficients
and provided hash codes for checking them...)
*/
if (fabs(q) <= .425) {/* 0.075 <= p <= 0.925 */
r = .180625 - q * q;
val =
q * (((((((r * 2509.0809287301226727 +
33430.575583588128105) * r + 67265.770927008700853) * r +
45921.953931549871457) * r + 13731.693765509461125) * r +
1971.5909503065514427) * r + 133.14166789178437745) * r +
3.387132872796366608)
/ (((((((r * 5226.495278852854561 +
28729.085735721942674) * r + 39307.89580009271061) * r +
21213.794301586595867) * r + 5394.1960214247511077) * r +
687.1870074920579083) * r + 42.313330701600911252) * r + 1.);
}
else { /* closer than 0.075 from {0,1} boundary */
/* r = min(p, 1-p) < 0.075 */
if (q > 0)
r = R_DT_CIv(p);/* 1-p */
else
r = p_;/* = R_DT_Iv(p) ^= p */
r = sqrt(- ((log_p &&
((lower_tail && q <= 0) || (!lower_tail && q > 0))) ?
p : /* else */ log(r)));
/* r = sqrt(-log(r)) <==> min(p, 1-p) = exp( - r^2 ) */
if (r <= 5.) { /* <==> min(p,1-p) >= exp(-25) ~= 1.3888e-11 */
r += -1.6;
val = (((((((r * 7.7454501427834140764e-4 +
.0227238449892691845833) * r + .24178072517745061177) *
r + 1.27045825245236838258) * r +
3.64784832476320460504) * r + 5.7694972214606914055) *
r + 4.6303378461565452959) * r +
1.42343711074968357734)
/ (((((((r *
1.05075007164441684324e-9 + 5.475938084995344946e-4) *
r + .0151986665636164571966) * r +
.14810397642748007459) * r + .68976733498510000455) *
r + 1.6763848301838038494) * r +
2.05319162663775882187) * r + 1.);
}
else { /* very close to 0 or 1 */
r += -5.;
val = (((((((r * 2.01033439929228813265e-7 +
2.71155556874348757815e-5) * r +
.0012426609473880784386) * r + .026532189526576123093) *
r + .29656057182850489123) * r +
1.7848265399172913358) * r + 5.4637849111641143699) *
r + 6.6579046435011037772)
/ (((((((r *
2.04426310338993978564e-15 + 1.4215117583164458887e-7)*
r + 1.8463183175100546818e-5) * r +
7.868691311456132591e-4) * r + .0148753612908506148525)
* r + .13692988092273580531) * r +
.59983220655588793769) * r + 1.);
}
if(q < 0.0)
val = -val;
/* return (q >= 0.)? r : -r ;*/
}
return mu + sigma * val;
}
double qgamma(double p, double alpha, double scale, int lower_tail, int log_p)
/* shape = alpha */
{
#define C7 4.67
#define C8 6.66
#define C9 6.73
#define C10 13.32
#define EPS1 1e-2
#define EPS2 5e-7/* final precision */
#define MAXIT 1000/* was 20 */
#define pMIN 1e-100 /* was 0.000002 = 2e-6 */
#define pMAX (1-1e-12)/* was 0.999998 = 1 - 2e-6 */
const double
i420 = 1./ 420.,
i2520 = 1./ 2520.,
i5040 = 1./ 5040;
double p_, a, b, c, ch, g, p1, v;
double p2, q, s1, s2, s3, s4, s5, s6, t, x;
int i;
/* test arguments and initialise */
#ifdef IEEE_754
if (ISNAN(p) || ISNAN(alpha) || ISNAN(scale))
return p + alpha + scale;
#endif
R_Q_P01_check(p);
if (alpha <= 0) ML_ERR_return_NAN;
/* FIXME: This (cutoff to {0, +Inf}) is far from optimal when log_p: */
p_ = R_DT_qIv(p);/* lower_tail prob (in any case) */
if (/* 0 <= */ p_ < pMIN) return 0;
if (/* 1 >= */ p_ > pMAX) return BOOM::infinity();
v = 2*alpha;
c = alpha-1;
g = lgammafn(alpha);/* log Gamma(v/2) */
/*----- Phase I : Starting Approximation */
#ifdef DEBUG_qgamma
REprintf("qgamma(p=%7g, alpha=%7g, scale=%7g, l.t.=%2d, log_p=%2d): ",
p,alpha,scale, lower_tail, log_p);
#endif
if(v < (-1.24)*R_DT_log(p)) { /* for small chi-squared */
#ifdef DEBUG_qgamma
REprintf(" small chi-sq.\n");
#endif
/* FIXME: Improve this "if (log_p)" :
* (A*exp(b)) ^ 1/al */
ch = pow(p_* alpha*exp(g+alpha*M_LN2), 1/alpha);
if(ch < EPS2) {/* Corrected according to AS 91; MM, May 25, 1999 */
goto END;
}
} else if(v > 0.32) { /* using Wilson and Hilferty estimate */
x = qnorm(p, 0, 1, lower_tail, log_p);
p1 = 0.222222/v;
ch = v*pow(x*sqrt(p1)+1-p1, 3);
#ifdef DEBUG_qgamma
REprintf(" v > .32: Wilson-Hilferty; x = %7g\n", x);
#endif
/* starting approximation for p tending to 1 */
if( ch > 2.2*v + 6 )
ch = -2*(R_DT_Clog(p) - c*log(0.5*ch) + g);
} else { /* for v <= 0.32 */
ch = 0.4;
a = R_DT_Clog(p) + g + c*M_LN2;
#ifdef DEBUG_qgamma
REprintf(" v <= .32: a = %7g\n", a);
#endif
do {
q = ch;
p1 = 1. / (1+ch*(C7+ch));
p2 = ch*(C9+ch*(C8+ch));
t = -0.5 +(C7+2*ch)*p1 - (C9+ch*(C10+3*ch))/p2;
ch -= (1- exp(a+0.5*ch)*p2*p1)/t;
} while(fabs(q - ch) > EPS1*fabs(ch));
}
#ifdef DEBUG_qgamma
REprintf("\t==> ch = %10g:", ch);
#endif
/*----- Phase II: Iteration
* Call pgamma() [AS 239] and calculate seven term taylor series
*/
for( i=1 ; i <= MAXIT ; i++ ) {
q = ch;
p1 = 0.5*ch;
p2 = p_ - pgamma(p1, alpha, 1, /*lower_tail*/true, /*log_p*/false);
#ifdef IEEE_754
if(!R_FINITE(p2))
#else
if(errno != 0)
#endif
return numeric_limits<double>::quiet_NaN();
t = p2*exp(alpha*M_LN2+g+p1-c*log(ch));
b = t/ch;
a = 0.5*t - b*c;
s1 = (210+a*(140+a*(105+a*(84+a*(70+60*a))))) * i420;
s2 = (420+a*(735+a*(966+a*(1141+1278*a)))) * i2520;
s3 = (210+a*(462+a*(707+932*a))) * i2520;
s4 = (252+a*(672+1182*a)+c*(294+a*(889+1740*a))) * i5040;
s5 = (84+2264*a+c*(1175+606*a)) * i2520;
s6 = (120+c*(346+127*c)) * i5040;
ch += t*(1+0.5*t*s1-b*c*(s1-b*(s2-b*(s3-b*(s4-b*(s5-b*s6))))));
if(fabs(q - ch) < EPS2*ch)
goto END;
}
ML_ERROR(ME_PRECISION);/* no convergence in MAXIT iterations */
END:
return 0.5*scale*ch;
}
double qbinom(double p, double n, double pr, int lower_tail, int log_p)
{
double q, mu, sigma, gamma, z, y;
#ifdef IEEE_754
if (ISNAN(p) || ISNAN(n) || ISNAN(pr))
return p + n + pr;
#endif
if(!R_FINITE(p) || !R_FINITE(n) || !R_FINITE(pr))
ML_ERR_return_NAN;
R_Q_P01_check(p);
if(n != floor(n + 0.5)) ML_ERR_return_NAN;
if (pr < 0 || pr > 1 || n < 0)
ML_ERR_return_NAN;
if (pr == 0. || n == 0) return 0.;
if (p == R_DT_0) return 0.;
if (p == R_DT_1) return n;
q = 1 - pr;
if(q == 0.) return n; /* covers the full range of the distribution */
mu = n * pr;
sigma = sqrt(n * pr * q);
gamma = (q - pr) / sigma;
#ifdef DEBUG_qbinom
REprintf("qbinom(p=%7g, n=%g, pr=%7g, l.t.=%d, log=%d): sigm=%g, gam=%g\n",
p,n,pr, lower_tail, log_p, sigma, gamma);
#endif
/* Note : "same" code in qpois.c, qbinom.c, qnbinom.c --
* FIXME: This is far from optimal [cancellation for p ~= 1, etc]: */
if(!lower_tail || log_p) {
p = R_DT_qIv(p); /* need check again (cancellation!): */
if (p == 0.) return 0.;
if (p == 1.) return n;
}
/* temporary hack --- FIXME --- */
if (p + 1.01*DBL_EPSILON >= 1.) return n;
/* y := approx.value (Cornish-Fisher expansion) : */
z = qnorm(p, 0., 1., /*lower_tail*/TRUE, /*log_p*/FALSE);
y = floor(mu + sigma * (z + gamma * (z*z - 1) / 6) + 0.5);
if(y > n) /* way off */ y = n;
#ifdef DEBUG_qbinom
REprintf(" new (p,1-p)=(%7g,%7g), z=qnorm(..)=%7g, y=%5g\n", p, 1-p, z, y);
#endif
z = pbinom(y, n, pr, /*lower_tail*/TRUE, /*log_p*/FALSE);
/* fuzz to ensure left continuity: */
p *= 1 - 64*DBL_EPSILON;
/*-- Fixme, here y can be way off --
should use interval search instead of primitive stepping down or up */
#ifdef maybe_future
if((lower_tail && z >= p) || (!lower_tail && z <= p)) {
#else
if(z >= p) {
#endif
/* search to the left */
#ifdef DEBUG_qbinom
REprintf("\tnew z=%7g >= p = %7g --> search to left (y--) ..\n", z,p);
#endif
for(;;) {
if(y == 0 ||
(z = pbinom(y - 1, n, pr, /*l._t.*/TRUE, /*log_p*/FALSE)) < p)
return y;
y = y - 1;
}
}
else { /* search to the right */
#ifdef DEBUG_qbinom
REprintf("\tnew z=%7g < p = %7g --> search to right (y++) ..\n", z,p);
#endif
for(;;) {
y = y + 1;
if(y == n ||
(z = pbinom(y, n, pr, /*l._t.*/TRUE, /*log_p*/FALSE)) >= p)
return y;
}
}
}
double qtukey(double p, double rr, double cc, double df,
int lower_tail, int log_p)
{
const double eps = 0.0001;
const int maxiter = 50;
double ans = 0.0, valx0, valx1, x0, x1, xabs;
int iter;
#ifdef IEEE_754
if (ISNAN(p) || ISNAN(rr) || ISNAN(cc) || ISNAN(df)) {
ML_ERROR(ME_DOMAIN);
return p + rr + cc + df;
}
#endif
R_Q_P01_check(p);
if (p == 1) ML_ERR_return_NAN;
/* df must be > 1 */
/* there must be at least two values */
if (df < 2 || rr < 1 || cc < 2) ML_ERR_return_NAN;
if (p == R_DT_0) return 0;
p = R_DT_qIv(p); /* lower_tail,non-log "p" */
/* Initial value */
x0 = qinv(p, cc, df);
/* Find prob(value < x0) */
valx0 = ptukey(x0, rr, cc, df, /*LOWER*/true, /*LOG_P*/false) - p;
/* Find the second iterate and prob(value < x1). */
/* If the first iterate has probability value */
/* exceeding p then second iterate is 1 less than */
/* first iterate; otherwise it is 1 greater. */
if (valx0 > 0.0)
x1 = std::max(0.0, x0 - 1.0);
else
x1 = x0 + 1.0;
valx1 = ptukey(x1, rr, cc, df, /*LOWER*/true, /*LOG_P*/false) - p;
/* Find new iterate */
for(iter=1 ; iter < maxiter ; iter++) {
ans = x1 - ((valx1 * (x1 - x0)) / (valx1 - valx0));
valx0 = valx1;
/* New iterate must be >= 0 */
x0 = x1;
if (ans < 0.0) {
ans = 0.0;
valx1 = -p;
}
/* Find prob(value < new iterate) */
valx1 = ptukey(ans, rr, cc, df, /*LOWER*/true, /*LOG_P*/false) - p;
x1 = ans;
/* If the difference between two successive */
/* iterates is less than eps, stop */
xabs = fabs(x1 - x0);
if (xabs < eps)
return ans;
}
/* The process did not converge in 'maxiter' iterations */
ML_ERROR(ME_NOCONV);
return ans;
}
// MM_R attribute_hidden
double qchisq_appr(double p, double nu, double g /* = log Gamma(nu/2) */,
logical lower_tail, logical log_p, double tol /* EPS1 */)
{
#define C7 4.67
#define C8 6.66
#define C9 6.73
#define C10 13.32
double alpha, a, c, ch, p1;
double p2, q, t, x;
/* test arguments and initialise */
#ifdef IEEE_754
if (ISNAN(p) || ISNAN(nu))
return p + nu;
#endif
R_Q_P01_check(p);
if (nu <= 0) ML_ERR_return_NAN;
alpha = 0.5 * nu;/* = [pq]gamma() shape */
c = alpha-1;
if(nu < (-1.24)*(p1 = R_DT_log(p))) { /* for small chi-squared */
/* log(alpha) + g = log(alpha) + log(gamma(alpha)) =
* = log(alpha*gamma(alpha)) = lgamma(alpha+1) suffers from
* catastrophic cancellation when alpha << 1
*/
double lgam1pa = (alpha < 0.5) ? lgamma1p(alpha) : (log(alpha) + g);
ch = exp((lgam1pa + p1)/alpha + M_LN2);
#ifdef DEBUG_qgamma
REprintf(" small chi-sq., ch0 = %g\n", ch);
#endif
} else if(nu > 0.32) { /* using Wilson and Hilferty estimate */
x = qnorm(p, 0, 1, lower_tail, log_p);
p1 = 2./(9*nu);
ch = nu*pow(x*sqrt(p1) + 1-p1, 3);
#ifdef DEBUG_qgamma
REprintf(" nu > .32: Wilson-Hilferty; x = %7g\n", x);
#endif
/* approximation for p tending to 1: */
if( ch > 2.2*nu + 6 )
ch = -2*(R_DT_Clog(p) - c*log(0.5*ch) + g);
} else { /* "small nu" : 1.24*(-log(p)) <= nu <= 0.32 */
ch = 0.4;
a = R_DT_Clog(p) + g + c*M_LN2;
#ifdef DEBUG_qgamma
REprintf(" nu <= .32: a = %7g\n", a);
#endif
do {
q = ch;
p1 = 1. / (1+ch*(C7+ch));
p2 = ch*(C9+ch*(C8+ch));
t = -0.5 +(C7+2*ch)*p1 - (C9+ch*(C10+3*ch))/p2;
ch -= (1- exp(a+0.5*ch)*p2*p1)/t;
} while(fabs(q - ch) > tol * fabs(ch));
}
return ch;
}
double qnbinom(double p, double n, double pr, int lower_tail, int log_p)
{
double P, Q, mu, sigma, gamma, z, y;
#ifdef IEEE_754
if (ISNAN(p) || ISNAN(n) || ISNAN(pr))
return p + n + pr;
#endif
R_Q_P01_check(p);
if (pr <= 0 || pr >= 1 || n <= 0) ML_ERR_return_NAN;
if (p == R_DT_0) return 0;
if (p == R_DT_1) return ML_POSINF;
Q = 1.0 / pr;
P = (1.0 - pr) * Q;
mu = n * P;
sigma = sqrt(n * P * Q);
gamma = (Q + P)/sigma;
/* Note : "same" code in qpois.c, qbinom.c, qnbinom.c --
* FIXME: This is far from optimal [cancellation for p ~= 1, etc]: */
if(!lower_tail || log_p) {
p = R_DT_qIv(p); /* need check again (cancellation!): */
if (p == R_DT_0) return 0;
if (p == R_DT_1) return ML_POSINF;
}
/* temporary hack --- FIXME --- */
if (p + 1.01*DBL_EPSILON >= 1.) return ML_POSINF;
/* y := approx.value (Cornish-Fisher expansion) : */
z = qnorm(p, 0., 1., /*lower_tail*/TRUE, /*log_p*/FALSE);
y = floor(mu + sigma * (z + gamma * (z*z - 1) / 6) + 0.5);
z = pnbinom(y, n, pr, /*lower_tail*/TRUE, /*log_p*/FALSE);
/* fuzz to ensure left continuity: */
p *= 1 - 64*DBL_EPSILON;
/*-- Fixme, here y can be way off --
should use interval search instead of primitive stepping down or up */
#ifdef maybe_future
if((lower_tail && z >= p) || (!lower_tail && z <= p)) {
#else
if(z >= p) {
#endif
/* search to the left */
for(;;) {
if(y == 0 ||
(z = pnbinom(y - 1, n, pr, /*l._t.*/TRUE, /*log_p*/FALSE)) < p)
return y;
y = y - 1;
}
}
else { /* search to the right */
for(;;) {
y = y + 1;
if((z = pnbinom(y, n, pr, /*l._t.*/TRUE, /*log_p*/FALSE)) >= p)
return y;
}
}
}
