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)length(n) > 1, the length
is taken to be the number required.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 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.dcauchy, pcauchy and qcauchy are all calculated
from numerically stable versions of the definitions. rcauchy uses inversion.
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 $x$.
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).