program logitlogistic
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(`sigma')) - (`sigma' - 1)*log(-1 + 1/$ML_y1) /// 
	- 2*`sigma'*log($ML_y1 ///
	+ exp(`mu'/`sigma')*(-1 + 1/$ML_y1)^(1/`sigma')*$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. 
*/