Cauchy                 package:stats                 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.

Source:

     'dcauchy', 'pcauchy' and 'qcauchy' are all calculated from
     numerically stable versions of the definitions.

     'rcauchy' uses inversion.

References:

     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.

See Also:

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

Examples:

     dcauchy(-1:4)

