What is Cauchy Distribution?

Also known as the Lorentz distribution. It has heavy tails and no defined mean or variance.

The tails fall off so slowly (1/x^2) that the integral for the mean does not converge.

x₀ is the Location parameter (peak). γ (Gamma) is the Scale parameter (half-width at half-maximum).

Cauchy Distribution Calculator

Calculate properties of the Lorentz distribution (undefined mean/variance).

Location (x₀)

Peak position

Scale (γ)

Half-width at half-max

Target Value (x)

CDF F(1)

PDF f(1) = 0

Mean

Undefined

Variance

Undefined

Formulas

PDF

CDF

Frequently Asked Questions

How to Use

What it calculates

This cauchy solves mathematical and statistical problems using standard formulas. Lorentz distribution (undefined mean).

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 Cauchy.

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