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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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