Right-truncating a lognormal distribution

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george pepper
george pepper 2019-8-18
编辑： Matt J 2019-8-18
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.
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george pepper
george pepper 2019-8-18
I think this is right. How can I code this?

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Matt J
Matt J 2019-8-18
编辑：Matt J 2019-8-18
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

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