program cauchitasinh 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) + log(1 + 2 * (-1 + $ML_y1) * $ML_y1) /// - log(4 * `sigma'^2 * (-1 + $ML_y1)^2 *$ML_y1^2 + (-1 + 2 * $ML_y1 /// + 2*`mu' * (-1 + $ML_y1) * $ML_y1)^2) } 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. */