program burr8burr7
version 13.0
args lnf Xb Xd
tempvar sigma
tempvar mu
quietly {
   gen double `sigma' = exp(`Xd')
   gen double `mu' = `Xb'
   replace `lnf' = -log(2*_pi*$ML_y1*`sigma' - 2*_pi*$ML_y1^2*`sigma') + log(1/cosh((`mu' + atanh(1 - 2* $ML_y1))/`sigma'))
   }
end
/*
This distribution is from the CDF-quantile family presented in 
Smithson, M. & Shou, Y. (2017). CDF-quantile distributions for modeling 
random variables on the unit interval. 
British Journal of Mathematical and Statistical Psychology, 70(3), 412-438. 
*/