program cauchitasinhouterv2
version 13
args lnf theta lsigma
tempvar sigma 
quietly gen double `sigma' = exp(`lsigma')
quietly replace `lnf' = ln((8*exp(`theta')*_pi*(1 - 2*$ML_y1 + 2*$ML_y1^2)*(`sigma'))/((1 - 4*$ML_y1 - 8*$ML_y1^3*(`sigma')^2 + 4*$ML_y1^4*(`sigma')^2 + 4*$ML_y1^2*(1 + (`sigma')^2))*((1 + exp(`theta'))*_pi - 2*(-1 + exp(`theta'))*atan((1 - 2*$ML_y1)/(2*$ML_y1*(`sigma') - 2*$ML_y1^2*(`sigma'))))^2)) /// 
   if $ML_y1 > 0 & $ML_y1 < 1
quietly replace `lnf' = ln(2*`sigma'*exp(`theta')/(_pi)) if $ML_y1 ==0
quietly replace `lnf' = ln(2*`sigma'/(_pi*exp(`theta'))) if $ML_y1 ==1
end