i calculated the integral with quad function and then used the log function for the result of the quad like this: proc nlp out=solve_x;   max chi_comma;   decvar x;   p_hat=CDF('NORMAL',(&gamma.-x*&r.)/((1-(&r.**2))**0.5),0,1);   chi=&d.*log(p_hat)+(&m.-&d.)*log(1-p_hat);   chi_comma=chi-(x**2)/2;   run; data _null_;   set solve_x;   call symput("theta", chi_comma);   run;   %put max of chi_comma is θ proc iml;   pi = constant("pi");   start toint(x);   p_hat=CDF('NORMAL',(&gamma.-x*&r.)/((1-(&r.**2))**0.5),0,1);   p=exp(&d.*log(p_hat)+(&m.-&d.)*log(1-p_hat)-&theta.-x**2/2);   return(p);   finish;   interval = .M || .P;   call quad(pm,"toint",interval);   print pm[format=E21.14];   psi=(log((1/((2*pi)**0.5))*pm)+&theta.);   print psi[format=E21.14];   quit; ... View more