program t2logistic
version 13.0
args lnf Xb Xd
tempvar sigma
tempvar mu
quietly {
	gen double `sigma' = exp(`Xd')
	gen double `mu' = `Xb'
	replace `lnf' = log(`sigma') -1/2 * log(2 + (`mu' + log(1 - $ML_y1) /// 
	- log($ML_y1))^2/`sigma'^2) -log(`mu'^2 + 2* `sigma'^2 -2* `mu' *(-log(1 - $ML_y1) /// 
	+ log($ML_y1)) + (-log(1 - $ML_y1) + log($ML_y1))^2) -log(1 - $ML_y1) - log($ML_y1)
	}
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. 
*/