Log-normal Distribution CDF Calculator

Log-normal Distribution CDF Calculator

For a log‑normal distribution with parameters \(\mu\) and \(\sigma\), the CDF is given by: $$ F(x;\mu,\sigma) = \Phi\!\Biggl(\frac{\ln(x)-\mu}{\sigma}\Biggr), $$ where \(\Phi(z)=0.5\Bigl[1+\operatorname{erf}\Bigl(\frac{z}{\sqrt{2}}\Bigr)\Bigr]\).

* Enter a value for \( x \) (with \( x>0 \)), the location parameter \(\mu\), and the scale parameter \(\sigma>0\).

Step 1: Enter Parameters

Enter a value for \( x \) (e.g., 1; must be > 0).

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 the CDF of \( X \) is:

$$ F(x;\mu,\sigma) = \Phi\!\Biggl(\frac{\ln(x)-\mu}{\sigma}\Biggr), $$ where \(\Phi(z)\) is the standard normal CDF.

Formula: \( F(x;\mu,\sigma) = \Phi\!\Bigl(\frac{\ln(x)-\mu}{\sigma}\Bigr) \)

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