program t2burr8
version 13.0
args lnf Xb Xd
tempvar sigma
tempvar mu
quietly {
	gen double `sigma' = exp(`Xd')
	gen double `mu' = `Xb'
	replace `lnf' = (log(_pi) + 2 * log(`sigma')) + log(1/sin(_pi * $ML_y1)) ///
	- (3/2) * log(`mu'^2 + 2 * `sigma'^2 - 2 * `mu' * log(tan((_pi * $ML_y1)/2)) ///
	+ log(tan((_pi * $ML_y1)/2))^2) 
	}
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. 
*/