double chi2_logp(double chi2, int dof)
/* Return the natural log probability corresponding to a chi^2 value */
/* of chi2 given dof degrees of freedom. */
{
double logp;
if (chi2 <= 0.0) {
return -INFINITY;
}
if (chi2 / dof > 15.0 || (dof > 150 && chi2 / dof > 6.0)) {
// printf("Using asymtotic expansion...\n");
// Use some asymtotic expansions for the chi^2 distribution
// this is eqn 26.4.19 of A & S
logp = log_asymtotic_incomplete_gamma(0.5 * dof, 0.5 * chi2) -
log_asymtotic_gamma(0.5 * dof);
} else {
int which, status;
double p, q, bound, df = dof, x = chi2;
which = 1;
status = 0;
/* Determine the basic probability */
cdfchi(&which, &p, &q, &x, &df, &status, &bound);
if (status) {
printf("\nError in cdfchi() (chi2_logp()):\n");
printf(" status = %d, bound = %g\n", status, bound);
printf(" p = %g, q = %g, x = %g, df = %g\n\n", p, q, x, df);
exit(1);
}
// printf("p = %.3g q = %.3g\n", p, q);
logp = log(q);
}
return logp;
}
double candidate_sigma(double power, int numsum, double numtrials)
/* Return the approximate significance in Gaussian */
/* sigmas of a candidate of numsum summed powers, */
/* taking into account the number of independent trials. */
{
double x = 0.0;
if (power <= 0.0) {
return 0.0;
}
if (power > 100.0) {
double logp;
/* Use some asymtotic expansions for the chi^2 distribution */
logp = log_asymtotic_incomplete_gamma(numsum, power) -
log_asymtotic_gamma(numsum);
/* Now adjust for the number of trials */
logp += log(numtrials);
/* Convert to a sigma */
x = extended_equiv_gaussian_sigma(logp);
} else {
int which, status;
double p, q, bound, mean = 0.0, sd = 1.0, shape, scale = 1.0;
which = 1;
status = 0;
shape = (double) numsum;
x = power;
/* Determine the basic probability */
cdfgam(&which, &p, &q, &x, &shape, &scale, &status, &bound);
if (status) {
printf("\nError in cdfgam() (candidate_sigma()):\n");
printf(" status = %d, bound = %g\n", status, bound);
printf(" p = %g, q = %g, x = %g, shape = %g, scale = %g\n\n",
p, q, x, shape, scale);
exit(1);
}
/* Adjust it for the number of trials */
if (p == 1.0)
q *= numtrials;
else
q = 1.0 - pow(p, numtrials);
p = 1.0 - q;
which = 2;
status = 0;
/* Convert to a sigma */
cdfnor(&which, &p, &q, &x, &mean, &sd, &status, &bound);
if (status) {
if (status == -2) {
x = 0.0;
} else if (status == -3) {
x = 38.5;
} else {
printf("\nError in cdfnor() (candidate_sigma()):\n");
printf(" status = %d, bound = %g\n", status, bound);
printf(" p = %g, q = %g, x = %g, mean = %g, sd = %g\n\n",
p, q, x, mean, sd);
exit(1);
}
}
}
if (x < 0.0)
return 0.0;
else
return x;
}
