program cauchitlogistic
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) + log(`sigma') - log(`mu'^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. 
*/