Log-normal Distribution PDF Calculator

Log-normal Distribution PDF Calculator

For a log‑normal distribution with parameters \(\mu\) and \(\sigma\), the PDF is given by: $$ f(x; \mu, \sigma) = \frac{1}{x\,\sigma\,\sqrt{2\pi}} \exp\!\Biggl(-\frac{(\ln x – \mu)^2}{2\sigma^2}\Biggr), \quad x > 0. $$

* Enter \( x \) (must be \(> 0\)), \(\mu\) (location parameter), and \(\sigma\) (scale parameter, \(\sigma > 0\)).

Step 1: Enter Parameters

Enter a value for \( x \) (must be > 0).

e.g., 0

e.g., 1 (must be > 0)

How It Works

The log‑normal distribution is defined for \( x > 0 \) as the distribution of a random variable whose logarithm is normally distributed.

Its PDF is given by: $$ f(x; \mu, \sigma) = \frac{1}{x\,\sigma\,\sqrt{2\pi}} \exp\!\Biggl(-\frac{(\ln x – \mu)^2}{2\sigma^2}\Biggr). $$

Simply enter the value of \( x \), and the parameters \(\mu\) and \(\sigma\) to compute the probability density.

Formula: \( f(x; \mu, \sigma) = \frac{1}{x\,\sigma\,\sqrt{2\pi}} \exp\!\Biggl(-\frac{(\ln x – \mu)^2}{2\sigma^2}\Biggr) \)

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