program burr7cauchy
version 13.0
args lnf Xb Xd
tempvar sigma
tempvar mu
quietly {
   gen double `sigma' = exp(`Xd')
   gen double `mu' = `Xb'
   replace `lnf' = - log((2*`sigma')/_pi) + 2*log(1/sin(_pi*$ML_y1)) ///
				+ 2*log(1/cosh((`mu' + 1/tan(_pi*$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. 
*/