program t2t2innerw3
version 13
args lnf mu theta lsigma
tempvar sigma 
quietly gen double `sigma' = exp(`lsigma')
quietly replace `lnf' = ln(-(cosh((`theta') + asinh((-1 + 2*$ML_y1)/(sqrt(2)*sqrt(-((-1 + $ML_y1)*$ML_y1)))))/(2*(-1 + $ML_y1)*$ML_y1*sqrt(1 - 2*$ML_y1 + 2*$ML_y1^2)*(`sigma')*(((`mu')^2 + 2*(`sigma')^2 - 2*(`mu')*sinh((`theta') + asinh((-1 + 2*$ML_y1)/(sqrt(2)*sqrt(-((-1 + $ML_y1)*$ML_y1))))) + sinh((`theta') + asinh((-1 + 2*$ML_y1)/(sqrt(2)*sqrt(-((-1 + $ML_y1)*$ML_y1)))))^2)/(`sigma')^2)^(3/2)))) /// 
   if $ML_y1 > 0 & $ML_y1 < 1
quietly replace `lnf' = ln(`sigma'^2*exp(2*`theta')) if $ML_y1 ==0
quietly replace `lnf' = ln(`sigma'^2/(exp(2*`theta'))) if $ML_y1 ==1
end