double normqtlQ (double prob, double mean, double var)
{ /* --- quantile of normal distrib. */
assert((var > 0) /* check the function arguments */
&& (prob >= 0) && (prob <= 1));
if (var == 1) return mean -unitqtlP(prob);
return mean -unitqtlP(prob) *sqrt(var);
} /* normqtlQ() */
double GammaqtlP (double prob, double k, double theta)
{ /* --- quantile of Gamma distribution */
int n = 0; /* loop variable */
double x, f, a, d, dx, dp; /* buffers */
assert((k > 0) && (theta > 0) /* check the function arguments */
&& (prob >= 0) && (prob <= 1));
if (prob >= 1.0) return INFINITY;
if (prob <= 0.0) return 0; /* handle limiting values */
if (prob < 0.05) x = exp(logGamma(k) +log(prob) /k);
else if (prob > 0.95) x = logGamma(k) -log1p(-prob);
else { /* distinguish three prob. ranges */
f = unitqtlP(prob); a = sqrt(k);
x = (f >= -a) ? a *f +k : k;
} /* compute initial approximation */
do { /* Lagrange's interpolation */
dp = prob -GammacdfP(x, k, 1);
if ((dp == 0) || (++n > 33)) break;
f = Gammapdf(x, k, 1);
a = 2 *fabs(dp/x);
a = dx = dp /((a > f) ? a : f);
d = -0.25 *((k-1)/x -1) *a*a;
if (fabs(d) < fabs(a)) dx += d;
if (x +dx > 0) x += dx;
else x /= 2;
} while (fabs(a) > 1e-10 *x);
if (fabs(dp) > EPS_QTL *prob) return -1;
return x *theta; /* check for convergence and */
} /* GammaqtlP() */ /* return the computed quantile */
