program burr8burr8
version 13.0
args lnf Xb Xd
tempvar sigma
tempvar mu
quietly {
   gen double `sigma' = exp(`Xd')
   gen double `mu' = `Xb'
   replace `lnf' = (`mu' + `sigma'*log(2) + `sigma'*log(1/sin(_pi*$ML_y1)) ///
   + log(tan(_pi*$ML_y1/2)) - `sigma'*log(exp((2*`mu')/`sigma')*`sigma' ///
   + `sigma'*tan((_pi*$ML_y1)/2)^(2/`sigma')))/`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. 
*/