Log-normal Distribution Sample Generator

Log‑normal Distribution Sample Generator

Generate random samples from a log‑normal distribution. If \(X \sim N(\mu, \sigma^2)\), then \(Y = \exp(X)\) follows a log‑normal distribution.

* Enter the location parameter \(\mu\), the scale parameter \(\sigma\) (with \(\sigma > 0\)), and the number of samples to generate.

Step 1: Enter Parameters

e.g., 0

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

e.g., 10

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: $$ Y = \exp\Bigl(\mu + \sigma Z\Bigr), $$ repeating the process for the desired sample size.

Formula: \( Y = \exp\Bigl(\mu + \sigma Z\Bigr) \), where \(Z\) is standard normal.

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