ICDF for values very close to one

Hey,

I have a problem where I have to transform random variables from the standard normal space to some other, arbitrary distribution.

They way I do this is the following: Given a standard normal random variable U, I compute the standard normal CDF to then use the inverse CDF of the target distribution to get the random variable X:

where is the ICDF of the target distribution and Φ is the standard normal CDF.

The issue I now face is that when Uis quite large (e.g. 10), the standard normal CDF function "normcdf" returns 1. This, however, leads to .

How do I solve this problem? I know that "normcdf" has the option normcdf(U, 'upper') to get instead of P but still - how do I get X?

I'd appreciate your help!

Cheers,

Cedric