Cauchy {base} | 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 to generate. |
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 / (pi 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.
dt
for the t distribution which generalizes
dcauchy(*, l = 0, s = 1)
.
all.equal(dcauchy(-1:4), 1 / (pi*(1 + (-1:4)^2)))