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