double pnorm5(double x, double mu, double sigma, int lower_tail, int log_p)
{
double p, cp;
/* Note: The structure of these checks has been carefully thought through.
* For example, if x == mu and sigma == 0, we get the correct answer 1.
*/
#ifdef IEEE_754
if(ISNAN(x) || ISNAN(mu) || ISNAN(sigma))
return x + mu + sigma;
#endif
if(!R_FINITE(x) && mu == x) return ML_NAN;/* x-mu is NaN */
if (sigma <= 0) {
if(sigma < 0) ML_ERR_return_NAN;
/* sigma = 0 : */
return (x < mu) ? R_DT_0 : R_DT_1;
}
p = (x - mu) / sigma;
if(!R_FINITE(p))
return (x < mu) ? R_DT_0 : R_DT_1;
x = p;
pnorm_both(x, &p, &cp, (lower_tail ? 0 : 1), log_p);
return(lower_tail ? p : cp);
}
double
pnorm(double x, double mu, double sigma, int lower_tail, int log_p){
double p, cp;
if (sigma == 0)
return (x < mu) ? 0.0 : 1.0;
p = (x - mu) / sigma;
x = p;
pnorm_both(x, &p, &cp, (lower_tail ? 0 : 1), log_p);
return(lower_tail ? p : cp);
}
double wmw_test_stat(double rankSum, int nInds, int nTotal, double tieCoef, TestType type) {
double uStat, mu, sigma2, zval, pgt, plt;
double res;
int nBg = nTotal-nInds;
uStat = nInds*nBg+nInds*(nInds+1.0)*0.5-rankSum;
if(type == U) {
res = uStat;
} else {
mu = (double)nInds*nBg*0.5; // NOT mu=n1*n2*0.5
sigma2 = nInds*nBg*(nTotal+1.0)/12.0*tieCoef; //NOT sigma2 = n1*n2*(n+1)/12*tieCoef
if(type == greater || type == abslog10greater) { /* greater */
zval = (uStat+0.5-mu)/sqrt(sigma2); // z lower tail
pnorm_both(zval, &pgt, &plt, 0, 0);
res = type==greater ? pgt : ABSLOG(pgt);
} else if (type == less || type == log10less) { /* less */
zval = (uStat-0.5-mu)/sqrt(sigma2); // z higher tail
pnorm_both(zval, &pgt, &plt, 1, 0);
res = type==less ? plt : log10(plt);
} else if (type == twoSided || type == abslog10twoSided || type == Q) { /* two sided*/
zval = (uStat-mu-(uStat>mu ? 0.5 : -0.5))/sqrt(sigma2);
pnorm_both(zval, &pgt, &plt, 2, 0);
res = mu==0.0 ? 1.0 : 2.0*MIN(pgt, plt);
if(type == abslog10twoSided) {
res = ABSLOG(res);
} else if (type == Q) {
res = pgt<=plt ? ABSLOG(res) : -ABSLOG(res);
}
} else {
error("Unrecognized type %d. Should not happen\n",
type);
}
}
return(res);
}
double pnorm(double x, double mu, double sigma, int lower_tail, int log_p)
{
double p, cp;
/* Note: The structure of these checks has been carefully thought through.
* For example, if x == mu and sigma == 0, we still get the correct answer.
*/
#ifdef IEEE_754
if(ISNAN(x) || ISNAN(mu) || ISNAN(sigma))
return x + mu + sigma;
#endif
if (sigma < 0) ML_ERR_return_NAN;
x = (x - mu) / sigma;
if(!R_FINITE(x)) {
if(ISNAN(x)) /* e.g. x=mu=Inf */ return(numeric_limits<double>::quiet_NaN());
if(x < 0) return R_DT_0;
else return R_DT_1;
}
pnorm_both(x, &p, &cp, (lower_tail ? 0 : 1), log_p);
return(lower_tail ? p : cp);
}
