MATLAB: Right-truncating a lognormal distribution

Question

Hello,

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.,

P(e< log(a)-x*beta),

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.

Answer 1

I think this is right. How can I code this?

function out=conditionalCDF(a,b,x,beta,sigma)
    pa=normcdf(log(a)-x*beta,0,sigma);
    pb=normcdf(log(b)-x*beta,0,sigma);
    out=min(1, pa./pb);
end