I would like to compute the probability that P(z<a) where
z=exp(x*beta+e) and e is distributed iid N(0,sigma^2).
I would like to evaluate the CDF of z, i.e.,
for various values of x*beta. However, I know that z cannot take a value greater than a certain number, b. How can I obtain the truncated distribution to evaluate the above probability?
Many thanks in advance.