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 |
lower.tail |
logical; if |
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
gives the density,
pcauchy
is the cumulative distribution function, and
qcauchy
is the quantile function of the Cauchy distribution.
rcauchy
generates random deviates.
The length of the result is determined by n
for
rcauchy
, and is the maximum of the lengths of the
numerical arguments for the other functions.
The numerical arguments other than n
are recycled to the
length of the result. Only the first elements of the logical
arguments are used.
Source
dcauchy
, pcauchy
and qcauchy
are all calculated
from numerically stable versions of the definitions.
rcauchy
uses inversion.
References
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 1, chapter 16. Wiley, New York.
See Also
Distributions for other standard distributions, including
dt
for the t
distribution which generalizes
dcauchy(*, l = 0, s = 1)
.
Examples
dcauchy(-1:4)