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/* Compute the CDF of the Tukey-Lambda distribution
using a braketing search with special checks
The PPF of the Tukey-lambda distribution is
G(p) = p**lam + (1-p)**lam / lam
Author: Travis Oliphant
*/
#include <math.h>
#define SMALLVAL 1e-4
#define EPS 1.0e-14
#define MAXCOUNT 60
double tukeylambdacdf(double x, double lmbda)
{
double pmin, pmid, pmax, plow, phigh, xeval;
int count;
xeval = 1.0/lmbda;
if (lmbda > 0.0) {
if (x < (-xeval)) return 0.0;
if (x > xeval) return 1.0;
}
if ((-SMALLVAL < lmbda) && (lmbda < SMALLVAL)) {
if (x >= 0) return 1.0/(1.0+exp(-x));
else return exp(x) / (1.0+exp(x));
}
pmin = 0.0;
pmid = 0.5;
pmax = 1.0;
plow = pmin;
phigh = pmax;
count = 0;
while ((count < MAXCOUNT) && (fabs(pmid-plow) > EPS)) {
xeval = (pow(pmid, lmbda) - pow(1.0-pmid,lmbda))/lmbda;
if (xeval == x) return pmid;
if (xeval > x) {
phigh = pmid;
pmid = (pmid + plow)/2.0;
}
else {
plow = pmid;
pmid = (pmid + phigh)/2.0;
}
count++;
}
return pmid;
}
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