Cauchy                 package:base                 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 `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].

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) = 1 / (pi s (1 + ((x-l)/s)^2))

     for all x.

Value:

     `dcauchy', `pcauchy', and `qcauchy' are respectively the density,
     distribution function and quantile function of the Cauchy
     distribution.  `rcauchy' generates random deviates from the
     Cauchy.

See Also:

     `dt' for the t distribution which generalizes `dcauchy(*, l = 0, s
     = 1)'.

Examples:

     all.equal(dcauchy(-1:4), 1 / (pi*(1 + (-1:4)^2)))

