pi=acos(-1.0);
// Test special cases
nu1=1.0; nu2=1.0; u=1.0;
Fdist norm1=new Fdist(nu1,nu2);
localflag = abs(norm1.p(u)-0.5/pi) > sbeps;
globalflag = globalflag || localflag;
if (localflag) {
fail("*** Fdist: Special case #1 failed");
}
nu1=1.0; nu2=2.0; u=1.0;
Fdist norm2=new Fdist(nu1,nu2);
localflag = abs(norm2.p(u)-1.0/pow(3.0,1.5)) > sbeps;
globalflag = globalflag || localflag;
if (localflag) {
fail("*** Fdist: Special case #2 failed");
}
nu1=2.0; nu2=1.0; u=1.0;
Fdist norm3=new Fdist(nu1,nu2);
localflag = abs(norm3.p(u)-1.0/pow(3.0,1.5)) > sbeps;
globalflag = globalflag || localflag;
if (localflag) {
fail("*** Fdist: Special case #3 failed");
}
nu1=2.0; nu2=2.0; u=1.0;
Fdist norm4=new Fdist(nu1,nu2);
localflag = abs(norm4.p(u)-0.25) > sbeps;
globalflag = globalflag || localflag;
if (localflag) {
fail("*** Fdist: Special case #4 failed");
}
nu1=2.0; nu2=2.0; u=2.0;
Fdist norm5=new Fdist(nu1,nu2);
localflag = abs(norm5.p(u)-1.0/9.0) > sbeps;
globalflag = globalflag || localflag;
if (localflag) {
fail("*** Fdist: Special case #5 failed");
}
// integral of distribution is one
sbeps=5.e-7;
nu1=5.0; nu2=5.0;
func_Fdist dist = new func_Fdist(nu1,nu2);
Midpnt q2 = new Midpnt(dist,0.0,10.0);
Midinf q3 = new Midinf(dist,10.0,1.0e99);
integral=qromo(q2)+qromo(q3);
localflag = abs(1.0-integral) > sbeps;
// System.out.printf(setprecision(15) << 1.0-integral);
globalflag = globalflag || localflag;
if (localflag) {
fail("*** Fdist: Distribution is not normalized to 1.0");
}
// cdf agrees with incomplete integral
sbeps=1.e-6;
nu1=5.0; nu2=5.0;
func_Fdist dist2 = new func_Fdist(nu1,nu2);
Fdist normcdf=new Fdist(nu1,nu2);
localflag=false;
for (i=0;i<N;i++) {
q2 = new Midpnt(dist2,0.0,x[i]);
integral=qromo(q2);
c[i]=integral;
d[i]=normcdf.cdf(x[i]);
// System.out.printf(c[i]-d[i]);
localflag = localflag || abs(c[i]-d[i]) > sbeps;
}
globalflag = globalflag || localflag;
if (localflag) {
fail("*** Fdist: cdf does not agree with result of quadrature");
}
// inverse cdf agrees with cdf
nu1=5.0; nu2=5.0;
Fdist normc=new Fdist(nu1,nu2);
Ran myran = new Ran(17);
sbeps=5.0e-14;
localflag=false;
for (i=0;i<1000;i++) {
u=3.0*myran.doub();
a=normc.cdf(u);
b=normc.invcdf(a);
// if (abs(u-b) > sbeps) {
// System.out.printf(setprecision(15) << u << " %f\n", b << " %f\n", abs(u-b));
// }
localflag = localflag || abs(u-b) > sbeps;
}
globalflag = globalflag || localflag;
if (localflag) {
fail("*** Fdist: Inverse cdf does not accurately invert the cdf");
}
// Fingerprint test
nu1=3.0; nu2=3.0;
Fdist normf=new Fdist(nu1,nu2);
for (i=0;i<N;i++) {
p[i]=normf.p(x[i]);
// System.out.printf(setprecision(17) << p[i] << " %f\n", pexp[i]);
}
// System.out.println("Fdist: Maximum discrepancy = %f\n", maxel(vecsub(p,pexp)));
localflag = maxel(vecsub(p,pexp)) > sbeps;
globalflag = globalflag || localflag;