Log‑normal Distribution Mean Calculator
For a log‑normal distribution with parameters \(\mu\) and \(\sigma\), the mean is given by: $$ E[X] = \exp\!\Bigl(\mu + \frac{\sigma^2}{2}\Bigr). $$
* Enter the location parameter \(\mu\) and the scale parameter \(\sigma\) (with \(\sigma > 0\)).
Step 1: Enter Parameters
e.g., 0
e.g., 1 (must be > 0)
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:
$$ E[X] = \exp\!\Bigl(\mu + \frac{\sigma^2}{2}\Bigr). $$
Enter the parameters \(\mu\) and \(\sigma\) to compute the mean.