Cauchy {stats} | R Documentation |
Density, distribution function, quantile function and random
generation for the Cauchy distribution with location parameter
location
and scale parameter scale
.
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)
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 P[X ≤ x], otherwise, P[X > x]. |
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) = 1 / (π s (1 + ((x-l)/s)^2))
for all x.
dcauchy
, pcauchy
, and qcauchy
are respectively
the density, distribution function and quantile function of the Cauchy
distribution. rcauchy
generates random deviates from the
Cauchy.
The length of the result is determined by n
for
rcauchy
, and is the maximum of the lengths of the
numerical parameters for the other functions.
The numerical parameters other than n
are recycled to the
length of the result. Only the first elements of the logical
parameters are used.
dcauchy
, pcauchy
and qcauchy
are all calculated
from numerically stable versions of the definitions.
rcauchy
uses inversion.
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.
Distributions for other standard distributions, including
dt
for the t distribution which generalizes
dcauchy(*, l = 0, s = 1)
.
dcauchy(-1:4)