Description Usage Arguments Details Value See Also Examples
Note that the Cauchy distribution is the student's t distribution with one degree of freedom. The Cauchy distribution does not have a well defined mean or variance. Cauchy distributions often appear as priors in Bayesian contexts due to their heavy tails.
1 |
location |
The location parameter. Can be any real number. Defaults
to |
scale |
The scale parameter. Must be greater than zero (?). Defaults
to |
We recommend reading this documentation on https://alexpghayes.github.io/distributions3, where the math will render with additional detail and much greater clarity.
In the following, let X be a Cauchy variable with mean
location =
x_0 and scale
= γ.
Support: R, the set of all real numbers
Mean: Undefined.
Variance: Undefined.
Probability density function (p.d.f):
f(x) = 1 / (π γ (1 + ((x - x_0) / γ)^2)
Cumulative distribution function (c.d.f):
F(t) = arctan((t - x_0) / γ) / π + 1/2
Moment generating function (m.g.f):
Does not exist.
A Cauchy
object.
Other continuous distributions:
Beta()
,
ChiSquare()
,
Exponential()
,
Frechet()
,
GEV()
,
GP()
,
Gamma()
,
Gumbel()
,
LogNormal()
,
Logistic()
,
Normal()
,
RevWeibull()
,
StudentsT()
,
Tukey()
,
Uniform()
,
Weibull()
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 |
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.