| 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 length(n) > 1, the length
is taken to be the number required. |
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.
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.
dt for the t distribution which generalizes
dcauchy(*, l = 0, s = 1).
dcauchy(-1:4)