| Cauchy {stats} | R Documentation |
The Cauchy Distribution
Description
Density, distribution function, quantile function and random
generation for the Cauchy distribution with location parameter
location and scale parameter scale.
Usage
dcauchy(x, location = 0, scale = 1, log = FALSE)
pcauchy(q, location = 0, scale = 1, lower.tail = TRUE, log.p = FALSE)
qcauchy(p, location = 0, scale = 1, lower.tail = TRUE, log.p = FALSE)
rcauchy(n, location = 0, scale = 1)
Arguments
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations. If |
location, scale |
location and scale parameters. |
log, log.p |
logical; if TRUE, probabilities p are given as log(p). |
lower.tail |
logical; if TRUE (default), probabilities are
|
Details
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.
Value
dcauchy, pcauchy, and qcauchy are respectively
the density, distribution function and quantile function of the Cauchy
distribution. rcauchy generates random deviates from the
Cauchy.
References
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth \& Brooks/Cole.
See Also
dt for the t distribution which generalizes
dcauchy(*, l = 0, s = 1).
Examples
dcauchy(-1:4)