How It Works

The log‑normal distribution is the distribution of a random variable whose logarithm is normally distributed.

If $\ln (X)\sim N(\mu ,{\sigma }^2)$, then $X=\exp (X)$ follows a log‑normal distribution.

This calculator uses the Box‑Muller method to generate standard normal random variables $Z$ and then computes: $$Y=\exp (\mu +\sigma Z),$$ repeating the process for the desired sample size.