Lognormal Distribution Calculator

If a variable's logarithm is normal, the variable itself is lognormal — common for incomes and sizes.

How the Math Works

A lognormal distribution describes a random variable whose logarithm follows a normal distribution, making it ideal for modeling positive-valued data with right-skewed patterns. The mean is calculated as e raised to the power of (mu plus half sigma squared), while the median simplifies to e raised to mu. The parameter mu represents the location of the underlying normal distribution, and sigma measures its spread - together they define the shape and scale of the lognormal curve.

Practical Applications

Financial analysts use lognormal calculations to model stock prices and option pricing, where prices cannot be negative and often exhibit multiplicative growth patterns. Environmental scientists apply it to model pollutant concentrations or rainfall amounts, which naturally follow skewed distributions. Actuaries rely on lognormal models for insurance claims and lifetime data, where extreme positive values are possible but uncommon.

Day-to-Day Use

Understanding lognormal distributions helps you interpret real-world phenomena like income distributions, where most people earn moderate amounts but a few earn significantly more. It explains why house prices, city populations, and even the size of oil reserves often follow this pattern. This knowledge helps you make better financial decisions, understand economic inequality, and interpret statistical reports in news and research studies more critically.

Worked example

μ 1, σ 0.5 → mean ≈ 3.08, median ≈ 2.72.

FAQ