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#include <StatComparator.h>
Public Member Functions | |
| StatComparator () | |
| ~StatComparator () | |
Static Public Member Functions | |
| static double | fisher (double F, double nu1, double nu2) |
| static double | invFisher (double p, double nu1, double nu2) |
| static double | invStudent (double p, double nu) |
| static double | student (double t, double nu) |
Static Protected Member Functions | |
| static double | betacf (double a, double b, double x) |
| static double | betai (double a, double b, double x) |
| static double | gammln (double x) |
| QGpCoreTools::StatComparator::StatComparator | ( | ) | [inline] |
{}
| QGpCoreTools::StatComparator::~StatComparator | ( | ) | [inline] |
{}
| double QGpCoreTools::StatComparator::betacf | ( | double | a, |
| double | b, | ||
| double | x | ||
| ) | [static, protected] |
References EPS, FPMIN, MAXIT, and TRACE.
Referenced by betai().
{
TRACE;
int m, m2;
double aa,c,d,del,h,qab,qam,qap;
qab=a+b;
qap=a+1.0;
qam=a-1.0;
c=1.0;
d=1.0-qab*x/qap;
if(fabs(d) < FPMIN) d=FPMIN;
d=1.0/d;
h=d;
for(m=1;m<=MAXIT;m++) {
m2=2*m;
aa=m*(b-m)*x/ ((qam+m2)*(a+m2));
d=1.0+aa*d;
if(fabs(d) < FPMIN) d=FPMIN;
c=1.0+aa/c;
if(fabs(c) < FPMIN) c=FPMIN;
d=1.0/d;
h*=d*c;
aa= -(a+m)*(qab+m)*x/ ((a+m2)*(qap+m2));
d=1.0+aa*d;
if(fabs(d) < FPMIN) d=FPMIN;
c=1.0+aa/c;
if(fabs(c) < FPMIN) c=FPMIN;
d=1.0/d;
del=d*c;
h*=del;
if(fabs(del-1.0) < EPS) break;
}
if(m > MAXIT) printf("a or b too big, or MAXIT too small in StatComparator::betacf\n");
return h;
}
| double QGpCoreTools::StatComparator::betai | ( | double | a, |
| double | b, | ||
| double | x | ||
| ) | [static, protected] |
Incomplete Beta function (Numerical Recipes chapter 6.4) Is(a,b)=Bx(a,b)/B(a,b)=1/B(a,b,) Integral(0->x)[t^(a-1)*(1-t)^(b-1)*dt] for(a,b >0)
The Student and Fisher functions are calculated from this integral
References betacf(), QGpCoreTools::exp(), gammln(), QGpCoreTools::log(), and TRACE.
Referenced by fisher(), and student().
{
TRACE;
//printf("betai: a=%lf, b=%lf, x=%lf\n",a,b,x);
double bt;
if(x<0.0 || x> 1.0) {
printf("Bad x in routine StatComparator::betai\n");
return 0;
}
if(x==0.0 || x== 1.0) bt=0.0;
else bt=exp(gammln(a+b)-gammln(a)-gammln(b)+a*log(x)+b*log(1.0-x));
if(x< (a+1.0)/(a+b+2.0))
return bt*betacf(a,b,x)/a; // Use continued fraction directly
else
return 1.0-bt*betacf(b,a,1.0-x)/b; /* Use continued fraction after
making the symetry transf. */
}
| double QGpCoreTools::StatComparator::fisher | ( | double | F, |
| double | nu1, | ||
| double | nu2 | ||
| ) | [inline, static] |
F ditribution probability function (Numerical Recipes chapter 6.4) We calculate the function Q(F|nu1, nu2)
References betai(), and TRACE.
Referenced by invFisher().
| double QGpCoreTools::StatComparator::gammln | ( | double | x | ) | [static, protected] |
The gamma function (Numerical Recipes chapter 6.1) Returns the value ln(gamma(x)) for x>0
References QGpCoreTools::log(), and TRACE.
Referenced by betai().
{
TRACE;
double y,tmp,ser;
static double cof[6]={76.18009172947146,
-86.50532032941677,
24.01409824083091,
-1.231739572450155,
0.1208650973866179e-2,
-0.5395239384953e-5};
int j;
y=x;
tmp=x+5.5;
tmp-=(x+0.5)*log(tmp);
ser=1.000000000190015;
for(j=0;j<=5;j++) ser+=cof[j]/++y;
return -tmp+log(2.5066282746310005*ser/x);
}
| double QGpCoreTools::StatComparator::invFisher | ( | double | p, |
| double | nu1, | ||
| double | nu2 | ||
| ) | [static] |
The Fisher function calculate the probability for a certain degree of freedom and a certain threshold value of the random variable. This function inverse the relation, to obtain the threshold value as a function of the probability and the degree of freedom (as presented in usual tables)
References fisher(), and TRACE.
{
TRACE;
// if(p<0.001 || p>0.9) {
// printf("Probability out of range in StatComparator::invFisher\n");
// return 0;
// }
double f1, f2, f3, a3;
f1=0;
f2=10000.0;
f3=5000.0;
a3=fisher(f3,nu1,nu2);
int nit=0;
do {
nit++;
if(a3<p) f2=f3; else f1=f3;
f3=0.5*(f1+f2);
a3=fisher(f3,nu1,nu2);
//printf("t1=%lf t2=%lf t3=%lf a3=%lf\n",t1,t2,t3,a3);
} while(a3!=p && f2-f1>1e-10 && nit<100);
if(nit>=100)
printf("*** WARNING ***: cannot achieve a good precision, err=%lf\n",
fabs(a3-p));
return f3;
}
| double QGpCoreTools::StatComparator::invStudent | ( | double | p, |
| double | nu | ||
| ) | [static] |
The Student function calculate the probability for a certain degree of freedom and a certain threshold value of the random variable. This function inverse the relation, to obtain the threshold value as a function of the probability and the degree of freedom (as presented in usual tables)
References student(), and TRACE.
{
TRACE;
// if(p<0.001 || p>0.9) {
// printf("Probability out of range in StatComparator::invStudent\n");
// return 0;
// }
double t1, t2, t3, a3;
t1=0.125;
t2=700.0;
t3=350.0625;
a3=student(t3,nu);
int nit=0;
do {
nit++;
if(a3<p) t2=t3; else t1=t3;
t3=0.5*(t1+t2);
a3=student(t3,nu);
//printf("t1=%lf t2=%lf t3=%lf a3=%lf\n",t1,t2,t3,a3);
} while(a3!=p && t2-t1>1e-10 && nit<100);
if(nit>=100)
printf("*** WARNING ***: cannot achieve a good precision, err=%lf\n",
fabs(a3-p));
return t3;
}
| double QGpCoreTools::StatComparator::student | ( | double | t, |
| double | nu | ||
| ) | [inline, static] |
Student's ditribution probability function (Numerical Recipes chapter 6.4) We calculate the function A(t|nu)
References betai(), and TRACE.
Referenced by invStudent().
