# How to simulate a sample from log skew t distribution in R

How I can simulate a sample from log skew t distribution with lambda equals to 0?

I didn't find any packages can do it and I'm not so in order to write a function. Can someone help me to understand how to simulate a sample from that distribution?

• You can use the rst function in the sn package. – Stéphane Laurent Dec 10 '19 at 14:29
• that one is a skew t distribution, I'd like to have a log skew t distribution. At the moment I'm using rst function. Thank you so much for the comment! :) – TheAvenger Dec 10 '19 at 14:30
• The log-skew is not the exponential of the skew ? (as the log-normal is the exponential of the normal). – Stéphane Laurent Dec 10 '19 at 14:35

## 1 Answer

If $$U$$ is uniform between 0 and 1, and if $$F$$ is a cumulative distribution function, then the random variable $$X = F^{-1}(U)$$ has cumulative distribution function $$F$$. This result is known as the inverse probability integral transformation. Therefore, to generate a value from your distribution, it suffices to draw $$u$$ from $$U(0, 1)$$ and to make the inverse transformation $$F^{−1}(u)$$.

PS: I do not know how tractable is the cdf of the log skew t distribution.