program cauchitcauchyouterv3
version 13
args lnf mu theta lsigma
tempvar sigma 
quietly gen double `sigma' = exp(`lsigma')
quietly replace `lnf' = ln((4*exp(`theta')*_pi^2*(`sigma')*(1/sin(_pi*$ML_y1))^2)/(((1 + exp(`theta'))*_pi - 2*(-1 + exp(`theta'))*atan(((`mu') + (1/tan(_pi*$ML_y1)))/(`sigma')))^2*((`mu')^2 + (`sigma')^2 + 2*(`mu')*(1/tan(_pi*$ML_y1)) + (1/tan(_pi*$ML_y1))^2))) /// 
   if $ML_y1 > 0 & $ML_y1 < 1
quietly replace `lnf' = ln(`sigma'*exp(`theta')) if $ML_y1 ==0
quietly replace `lnf' = ln(`sigma'/(exp(`theta'))) if $ML_y1 ==1
end