ICDF for values very close to one

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Cedric Kotitschke
Cedric Kotitschke 2022 年 8 月 31 日
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:
X = icdf(normcdf(U))
where ICDF 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 X = infinity.
How do I solve this problem? I know that "normcdf" has the option normcdf(U, 'upper') to get 1-P instead of P but still - how do I get X?
I'd appreciate your help!

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