program logitasinh 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) - log(`sigma') - 2*log(exp(1/(`sigma' - `sigma'*$ML_y1)) /// + exp(`mu'/`sigma' + 1/(2*`sigma'*$ML_y1 - 2*`sigma'*($ML_y1^2)))) - 2*log(1 - $ML_y1) /// - 2*log($ML_y1) + log(1 - 2*$ML_y1 + 2*($ML_y1^2)) + 1/(2*`sigma'*$ML_y1 /// - 2*`sigma'*($ML_y1^2)) + 2*($ML_y1/(2*`sigma'*$ML_y1 - 2*`sigma'*($ML_y1^2))) /// + 2*`mu'*($ML_y1/(2*`sigma'*$ML_y1 - 2*`sigma'*($ML_y1^2))) - 2*`mu' * /// (($ML_y1^2)/(2*`sigma'*$ML_y1 - 2*`sigma'*($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. */