oneoverpi=1.0/pi;
sbeps=1.e-15;
// Test special cases
m=0; s=1; u=0;
Cauchydist norm1=new Cauchydist(m,s);
localflag = abs(norm1.p(u)-oneoverpi) > sbeps;
globalflag = globalflag || localflag;
if (localflag) {
fail("*** Cauchydist: Special case #1 failed");
}
m=1; s=1; u=m;
Cauchydist norm2=new Cauchydist(m,s);
localflag = abs(norm2.p(u)-oneoverpi) > sbeps;
globalflag = globalflag || localflag;
if (localflag) {
fail("*** Cauchydist: Special case #2 failed");
}
m=1; s=1; u=0;
Cauchydist norm3=new Cauchydist(m,s);
localflag = abs(norm3.p(u)-oneoverpi/2.0) > sbeps;
globalflag = globalflag || localflag;
if (localflag) {
fail("*** Cauchydist: Special case #3 failed");
}
m=1; s=2; u=1;
Cauchydist norm4=new Cauchydist(m,s);
localflag = abs(norm4.p(u)-oneoverpi/2.0) > sbeps;
globalflag = globalflag || localflag;
if (localflag) {
fail("*** Cauchydist: Special case #4 failed");
}
m=1; s=2; u=0;
Cauchydist norm5=new Cauchydist(m,s);
localflag = abs(norm5.p(u)-oneoverpi/2.0/(1+1.0/4.0)) > sbeps;
globalflag = globalflag || localflag;
if (localflag) {
fail("*** Cauchydist: Special case #5 failed");
}
// integral of distribution is one
sbeps=1.e-8;
m=1.0;s=2.0;
func_Cauchydist dist=new func_Cauchydist(m,s);
Midinf q1 = new Midinf(dist,-1.0e99,-1.0);
Midpnt q2 = new Midpnt(dist,-1.0,1.0);
Midinf q3 = new Midinf(dist,1.0,1.0e99);
integral=qromo(q1)+qromo(q2)+qromo(q3);
localflag = abs(1.0-integral) > sbeps;
// System.out.printf(setprecision(15) << 1.0-integral);
globalflag = globalflag || localflag;
if (localflag) {
fail("*** Cauchydist: Distribution is not normalized to 1.0");
}
// cdf agrees with incomplete integral
sbeps=1.e-7;
m=0.5;s=1.5;
func_Cauchydist dist2=new func_Cauchydist(m,s);
Cauchydist normcdf = new Cauchydist(m,s);
localflag=false;
for (i=0;i<N;i++) {
if (x[i] < 0.0) {
q1 = new Midinf(dist2,-1.e99,x[i]);
integral=qromo(q1);
} else {
q1 = new Midinf(dist2,-1.e99,-1.0);
q2 = new Midpnt(dist2,-1.0,x[i]);
integral=qromo(q1)+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("*** Cauchydist: cdf does not agree with result of quadrature");
}
// inverse cdf agrees with cdf
m=0.5;s=1.5;
Cauchydist normc=new Cauchydist(m,s);
Ran myran = new Ran(17);
sbeps=1.0e-14;
localflag=false;
for (i=0;i<1000;i++) {
u=m-3.0*s+6.0*s*myran.doub();
a=normc.cdf(u);
b=normc.invcdf(a);
// 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("*** Cauchydist: Inverse cdf does not accurately invert the cdf");
}
// Fingerprint test
m=0.5;s=1.5;
Cauchydist normf=new Cauchydist(m,s);
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("Cauchydist: Maximum discrepancy = %f\n", maxel(vecsub(p,pexp)));
localflag = maxel(vecsub(p,pexp)) > sbeps;
globalflag = globalflag || localflag;