Unit Loss Function

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   Standard Normal Unit Loss Function (UNL)

   solve UNL(x)=c
   for a given c

   Method: solve f(x) - x * (1-F(x)) = c
   where f is standard normal density function and F is the standard
   normal CDF.

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scalar c /0.0331/;

variable x;
equation e;

e..  1/sqrt(2*pi)*exp(-0.5*sqr(x)) - x * (1-errorf(x)) =e= c;

* initial value
x.l = 1;

model m /e/;
solve m using cns;
display x.l;