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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