program asinhasinhouterv2
version 13
args lnf theta lsigma
tempvar sigma 
quietly gen double `sigma' = exp(`lsigma')
quietly replace `lnf' = ln((exp((`theta') + asinh((1 - 2*$ML_y1)/(2*$ML_y1*(`sigma') ///
   - 2*$ML_y1^2*(`sigma'))))*(1 - 2*$ML_y1 + 2*$ML_y1^2))/((exp(`theta') + ///
   exp(asinh((1 - 2*$ML_y1)/(2*$ML_y1*(`sigma') - 2*$ML_y1^2*(`sigma')))))^2 ///
   *(-1 + $ML_y1)^2*$ML_y1^2*(`sigma')*sqrt((1 - 4*$ML_y1 - 8*$ML_y1^3*(`sigma')^2 ///
   + 4*$ML_y1^4*(`sigma')^2 + 4*$ML_y1^2*(1 + (`sigma')^2))/((-1 + $ML_y1)^2 ///
   *$ML_y1^2*(`sigma')^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