Log-normal Distribution Mean Calculator

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.

Formula: \( E[X] = \exp\!\Bigl(\mu + \frac{\sigma^2}{2}\Bigr) \)

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