Cauchy Distribution |
(continuous probab dist for equations) |
Usage: |
CauchyDist (x, m, s) |
Definition: |
1 / (p s (1 + ((x-m)/s)^2)) |
Parameters: |
m = location s = scale |
Required: |
s > 0 |
Moments: |
m = undefined s = undefined |
Although real-world data rarely follows a Cauchy distribution, it is useful because of its unusualness. For example, although it is symmetric about m (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.