I am coding some equations which involve lognormal and uniform variables. For instance, I have the following expression (let's call it first expression):
and then another expression (let's call this one second expression):
You will notice expression (2) is just expression (1) under double integral. Here, 
and 
are log-normally distributed, that is 
and 
, respectively. Further, 
follows a uniform distribution, i.e., 
and 
(it's a product of the two lognormal variables). In the second expression, the first expression is first integrated with respect to 
which follows a uniform distribution and then it's integrated a second time with respect to z which follows a lognormal distribution. I am struggling to figure out how to code them correctly. I will be most grateful for any help. Can I code them like this?
SB = (1 - logncdf*(xbar(+1)/z(+1)))*(xbar(+1)/z(+1)) + lognpdf(epsilon)
SBtilde = lognpdf(unipdf(SB, a, sigmabar))
If this will not work, is there something else I can do? Can I use an external function file? I thought about writing an external function file but then I reached my wit's end thinking about how to handle these integral limits and multiple integrals.
