dist_cauchy
The Cauchy distribution
Description
![[Maturing]](../help/figures/lifecycle-maturing.svg)
Usage
dist_cauchy(location, scale)
Arguments
location |
location and scale parameters. |
scale |
location and scale parameters. |
Details
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.
We recommend reading this documentation on https://pkg.mitchelloharawild.com/distributional/, where the math will render nicely.
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.
See Also
Examples
dist <- dist_cauchy(location = c(0, 0, 0, -2), scale = c(0.5, 1, 2, 1)) dist mean(dist) variance(dist) skewness(dist) kurtosis(dist) generate(dist, 10) density(dist, 2) density(dist, 2, log = TRUE) cdf(dist, 4) quantile(dist, 0.7)