program asinhcauchyouterw2
version 13
args lnf theta lsigma
tempvar sigma 
quietly gen double `sigma' = exp(`lsigma')
quietly replace `lnf' = ln((_pi*cosh((`theta') - asinh(1/tan(_pi*$ML_y1)/(`sigma')))* ///
   (1/sin(_pi*$ML_y1))^2)/(exp(asinh(sinh((`theta') - asinh(1/tan(_pi* ///
   $ML_y1)/(`sigma')))))*((1 + exp(-asinh(sinh((`theta') - asinh(1/tan(_pi* ///
   $ML_y1)/(`sigma'))))))^2*(`sigma')*sqrt(1 + (1/tan(_pi*$ML_y1))^2/(`sigma')^2)* ///
   sqrt(1 + sinh((`theta') - asinh(1/tan(_pi*$ML_y1)/(`sigma')))^2)))) /// 
   if $ML_y1 > 0 & $ML_y1 < 1
quietly replace `lnf' = ln(_pi*`sigma'*exp(`theta')/2) if $ML_y1 ==0
quietly replace `lnf' = ln(_pi*`sigma'/(exp(`theta')*2)) if $ML_y1 ==1
end