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. */