program logitburr8
version 13.0
args lnf Xb Xd
tempvar sigma
tempvar mu
quietly {
	gen double `sigma' = exp(`Xd')
	gen double `mu' = `Xb'
	replace `lnf' = log(1/sin(_pi*$ML_y1)) + ((`mu' + `sigma'*log(_pi) ///
	- `sigma'*log(`sigma')) + log(tan((_pi*$ML_y1)/2)) - 2*`sigma'*log(exp(`mu'/`sigma') ///
	+ tan((_pi*$ML_y1)/2)^(1/`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. 
*/