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;
}
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;
}
inline double dcdflib_chi_quantile(double p, double df)
{
int what = 2;
int status = 0;
double x, bound, q(1 - p);
cdfchi(&what, &p, &q, &x, &df, &status, &bound);
return x;
}
inline double dcdflib_chi_cdf(double x, double df)
{
int what = 1;
int status = 0;
double p, q, bound;
cdfchi(&what, &p, &q, &x, &df, &status, &bound);
return p;
}
void V_cdfchi(int *which, double *p, double *q, double *x, double *df,
int *status, double *bound, int *len)
{
int i;
for (i = 0; i < *len; i++) {
cdfchi((int *)which, &p[i], &q[i], &x[i], &df[i],
(int *)&status[i], &bound[i]);
}
}
double chistat(double x, double df)
{
double p, q, d1 = 1.0, bound;
int status, which = 1;
if (x == 0.0) return 1.0;
// if (x<0.0 && x>-1.0) return 1.0;
if (x<0.0) return 1.0;
/* do not worry about negative lrt values */
cdfchi(&which, &p, &q, &x, &df, &status, &bound);
if (status != 0)
dcerror(1,"cdfchi() failed in chistat(%f,%f)", x,df);
return q;
}
double QCHISQ(double p, int m)
{
int which, status;
double chisq, q, df, bound;
which = 2;
df = (double) m;
q = 1.0 - p;
cdfchi(&which, &p, &q, &chisq, &df, &status, &bound);
if (status == 0) return chisq;
else
{
Warning("Error in computing chi-square; returning -1");
return -1;
}
}
static int cdf_pchisq (lua_State *L) {
/* stack should contain x, df and opt. pnonc */
lua_Number x = luaL_checknumber(L, 1);
lua_Number df = luaL_checknumber(L, 2);
lua_Number pnonc = luaL_optnumber(L, 3, 0);
lua_Number p, q, bound;
int which = 1;
int status;
check_chisq(L, 1, x, df, pnonc);
if (pnonc==0) /* central? */
cdfchi(&which, &p, &q, &x, &df, &status, &bound);
else /* non-central */
cdfchn(&which, &p, &q, &x, &df, &pnonc, &status, &bound);
check_status(status, bound);
lua_pushnumber(L, p);
return 1;
}
static int cdf_qchisq (lua_State *L) {
/* stack should contain p, df and opt. pnonc */
lua_Number p = luaL_checknumber(L, 1);
lua_Number df = luaL_checknumber(L, 2);
lua_Number pnonc = luaL_optnumber(L, 3, 0);
lua_Number x;
check_chisq(L, 2, p, df, pnonc);
if (p==0 || p==1) x = (p==0) ? 0 : HUGE_VAL;
else {
lua_Number q = 1-p;
lua_Number bound;
int which = 2;
int status;
if (pnonc==0) /* central? */
cdfchi(&which, &p, &q, &x, &df, &status, &bound);
else /* non-central */
cdfchn(&which, &p, &q, &x, &df, &pnonc, &status, &bound);
check_status(status, bound);
}
lua_pushnumber(L, x);
return 1;
}
