| Cauchy {base} | R Documentation |
The Cauchy Distribution
Usage
dcauchy(x, location = 0, scale = 1)
pcauchy(q, location = 0, scale = 1)
qcauchy(p, location = 0, scale = 1)
rcauchy(n, location = 0, scale = 1)
Arguments
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations to generate. |
location, scale |
location and scale parameters. |
Value
These functions provide information about the Cauchy distribution with
location parameter location and scale parameter scale.
dcauchy, pcauchy, and qcauchy are respectively
the density, distribution function and quantile function of the Cauchy
distribution. rcauchy generates random deviates from the
Cauchy.
If location or scale are not specified, they assume
the default values of 0 and 1 respectively.
The Cauchy distribution with location l and scale s has
density
f(x) = \frac{1}{\pi s}
\left( 1 + \left(\frac{x - l}{s}\right)^2 \right)^{-1}%
for all x.
See Also
dt for the t distribution which generalizes
dcauchy(*, l = 0, s = 1).
Examples
all.equal(dcauchy(-1:4), 1 / (pi*(1 + (-1:4)^2)))