What is Log-Normal Distribution?

A random variable X is log-normally distributed if its natural logarithm ln(X) is normally distributed.

Modeling stock prices, income distribution, and latent periods of diseases.

μ (mu) and σ (sigma) are the mean and standard deviation of the variable's NATURAL LOGARITHM, not of X itself.

Log-Normal Distribution

Calculate properties where ln(X) follows a normal distribution.

Log-Scale (μ)

Mean of ln(X)

Shape (σ)

SD of ln(X)

Target Value (x)

x > 0

CDF F(1)

PDF f(1) = 0

Mean

Variance

Formulas

PDF

Mean

Variance

Frequently Asked Questions

How to Use

What it calculates

This log-normal solves mathematical and statistical problems using standard formulas. Models positive skewed data.

When to use it

Use for homework, data analysis, exam prep, or quick verification of manual calculations.

Example

Adjust the inputs above to model your specific scenario with the Log-Normal.

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