double power_for_sigma(double sigma, int numsum, double numtrials)
/* Return the approximate summed power level required */
/* to get a Gaussian significance of 'sigma', taking */
/* into account the number of independent trials. */
{
int which, status;
double p, q, x, bound, mean = 0.0, sd = 1.0, df, scale = 1.0;
which = 1;
status = 0;
x = sigma;
cdfnor(&which, &p, &q, &x, &mean, &sd, &status, &bound);
if (status) {
printf("\nError in cdfnor() (power_for_sigma()):\n");
printf(" cdfstatus = %d, bound = %g\n\n", status, bound);
printf(" p = %g, q = %g, x = %g, mean = %g, sd = %g\n\n", p, q, x, mean,
sd);
exit(1);
}
q = q / numtrials;
p = 1.0 - q;
which = 2;
df = 2.0 * numsum;
status = 0;
cdfchi(&which, &p, &q, &x, &df, &status, &bound);
if (status) {
printf("\nError in cdfchi() (power_for_sigma()):\n");
printf(" status = %d, bound = %g\n", status, bound);
printf(" p = %g, q = %g, x = %g, df = %g, scale = %g\n\n",
p, q, x, df, scale);
exit(1);
}
return 0.5 * x;
}
inline double dcdflib_norm_quantile(double p, double mean, double sd)
{
int what = 2;
int status = 0;
double x, bound, q(1 - p);
cdfnor(&what, &p, &q, &x, &mean, &sd, &status, &bound);
return x;
}
inline double dcdflib_norm_cdf(double x, double mean, double sd)
{
int what = 1;
int status = 0;
double p, q, bound;
cdfnor(&what, &p, &q, &x, &mean, &sd, &status, &bound);
return p;
}
void V_cdfnor(int *which, double *p, double *q, double *x, double *mean,
double *sd, int *status, double *bound, int *len)
{
int i;
for (i = 0; i < *len; i++) {
cdfnor((int *)which, &p[i], &q[i], &x[i], &mean[i],
&sd[i], (int *)&status[i], &bound[i]);
}
}
/********************************************************************
** CNORM--subfunction used to compute cumulative normal distribution.
*********************************************************************/
double
CNORM (double x)
{
int which, status;
double p, q, mean, sd, bound;
which = 1;
mean = 0.0;
sd = 1.0;
cdfnor(&which, &p, &q, &x, &mean, &sd, &status, &bound);
return(p);
}
static int stat_pnorm (lua_State *L) {
/* stack should contain x, and opt. mean and sd */
lua_Number x = luaL_checknumber(L, 1);
lua_Number mean = luaL_optnumber(L, 2, 0);
lua_Number sd = luaL_optnumber(L, 3, 1);
lua_Number p, q, bound;
int which = 1;
int status;
check_norm(L, 1, x, sd);
cdfnor(&which, &p, &q, &x, &mean, &sd, &status, &bound);
check_status(L, status, bound);
lua_pushnumber(L, p);
return 1;
}
static int cdf_qnorm (lua_State *L) {
/* stack should contain p, and opt. mean and sd */
lua_Number p = luaL_checknumber(L, 1);
lua_Number mean = luaL_optnumber(L, 2, 0);
lua_Number sd = luaL_optnumber(L, 3, 1);
lua_Number x;
check_norm(L, 2, p, sd);
if (p==0 || p==1) x = (p==0) ? -HUGE_VAL : HUGE_VAL;
else {
lua_Number q = 1-p;
lua_Number bound;
int which = 2;
int status;
cdfnor(&which, &p, &q, &x, &mean, &sd, &status, &bound);
check_status(status, bound);
}
lua_pushnumber(L, x);
return 1;
}
double equivalent_gaussian_sigma(double logp)
/* Return the approximate significance in Gaussian sigmas */
/* corresponding to a natural log probability logp */
{
double x;
if (logp < -600.0) {
x = extended_equiv_gaussian_sigma(logp);
} else {
int which, status;
double p, q, bound, mean = 0.0, sd = 1.0;
q = exp(logp);
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;
}
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;
}
