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Cauchy Distribution

(continuous probab dist for equations)

Usage:

CauchyDist (x, μ, σ)

Definition:

1 / (π σ (1 + ((x-μ)/σ)^2))

Parameters:

μ = location       σ = scale

Required:

σ > 0

Moments:

mean is undefined

std dev is undefined

Although real-world data rarely follows a Cauchy distribution, it is useful because of its unusualness.  For example, although it is symmetric about μ (which is therefore its median and mode), it doesn't have a mean (or variance, etc.) because the appropriate integrals don't converge.  

The C(0,1) distribution is also Student's t distribution with degrees of freedom = 1.

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