program cauchitcauchy
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') - log(`mu'^2 + `sigma'^2 + 2*`mu'/tan(_pi*$ML_y1) ///
	+ 1/tan(_pi*$ML_y1)^2) + 2*log(1/sin(_pi*$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.
*/