/* Tawn Copula(Asymmetric Logistic) in Extreme Value Family                */
/* C(u,v)=exp((1-a)*ln(u)+(1-b)*ln(v)-((-a*ln(u))^c+(-b*ln(v))^c)^(1/c))   */
/* Solve  q=exp((1-a)*ln(u)+(1-b)*ln(v)-((-a*ln(u))^c+(-b*ln(v))^c)^(1/c)) */
/*          .*( (1-a)/u-1/c*((-a*ln(u))^c+(-b*ln(v))^c)^(1/c-1)            */
/*               .*c.*(-a*ln(u))^(c-1).*(-a/u) )                  (=Cu)    */
/* in terms of v numerically. This is very slow.                           */                 
new; cls;
a=0.9;
b=0.9;
c=2;
n=1000;
U=Ctawn(a,b,c,n);

library pgraph;
graphset;
_plctrl=-1;
xy(U[.,1],U[.,2]);



proc Ctawn(a,b,c,n);
   local u,q,v;
   if a<0 or b<0 or a>1 or b>1;
      errorlog "ERROR: Parameter a and b must be 0<=a<=1 and 0<=b<=1";
      retp(".");
   endif;
   if a==0 and b==0;
      errorlog "ERROR: Parameter a and b must not equal to 0 at the same time.";
      retp(".");
   endif;
   if c<1;
      errorlog "ERROR: Parameter c must be c>=1";
      retp(".");
   endif;
   u=rndu(n,1);
   q=rndu(n,1);
   v=calcv(u,q,a,b,c);
   retp(u~v);
endp;

proc calcv(u,q,a,b,c);
   local vstar,vstarstar,i,v,x;
   vstar=zeros(rows(q),1);
   i=1;
   do while i<=rows(q);
      v=seqa(0.0001,0.0001,10000);
      x=abs(q[i]-Cu(u[i],v,a,b,c));
      vstar[i]=v[minindc(x)];
      v=seqa(vstar[i]-0.00005,0.00000001,10000);
      x=abs(q[i]-Cu(u[i],v,a,b,c));
      vstarstar=v[minindc(x)];
      if vstarstar==vstar[i]-0.00005;
         v=seqa(0.00000001,0.00000001,10000);
         x=abs(q[i]-Cu(u[i],v,a,b,c));
         vstar[i]=v[minindc(x)];
      else;
         vstar[i]=vstarstar;
      endif;
      if vstarstar>1;
         vstar[i]=1;
      endif;
      i=i+1;
   endo;
   retp(vstar);
endp;

fn Cu(u,v,a,b,c)=exp((1-a)*ln(u)+(1-b)*ln(v)-((-a*ln(u))^c+(-b*ln(v))^c)^(1/c))
                 .*( (1-a)/u-1/c*((-a*ln(u))^c+(-b*ln(v))^c)^(1/c-1)
                     .*c.*(-a*ln(u))^(c-1).*(-a/u) );