Log-normal Distribution Mode Calculator

Log‑normal Distribution Mode Calculator

For a log‑normal distribution where \(\ln(X) \sim N(\mu, \sigma^2)\), the mode is computed as: $$ \text{Mode} = \exp\bigl(\mu – \sigma^2\bigr). $$

* 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 describes a random variable whose logarithm is normally distributed: \(\ln(X) \sim N(\mu, \sigma^2)\).

The mode (i.e. the most likely value) of \(X\) is the value at which its PDF is maximized. For a log‑normal distribution, the mode is given by: $$ \text{Mode} = \exp\bigl(\mu – \sigma^2\bigr). $$

Formula: \( \text{Mode} = \exp\bigl(\mu – \sigma^2\bigr) \)

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