| 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., Wilks A. R. (1988). The New S Language. Chapman and Hall/CRC, London.
Johnson N. L., Kotz S., Balakrishnan N. (1994). Continuous Univariate Distributions, volume 1. Wiley, New York. ISBN 978-0-471-58495-7. Chapter 16.
See Also
Distributions for other standard distributions, including
dt for the t distribution which generalizes
dcauchy(*, l = 0, s = 1).
Examples
dcauchy(-1:4)