Cauchy Distribution
DESCRIPTION:
Density, cumulative probability, quantiles and random generation of the Cauchy distribution.
USAGE: 
dcauchy(x, location=0, scale=1)
pcauchy(q, location=0, scale=1)
qcauchy(p, location=0, scale=1)
rcauchy(n, location=0, scale=1)
REQUIRED ARGUMENTS:
x:
vector of quantiles. Missing values (NAs) are allowed.
q:
vector of quantiles. Missing values (NAs) are allowed.
p:
vector of probabilities. Missing values (NAs) are allowed.
n:
sample size. If length(n) is larger than 1, then length(n) random values are returned.
OPTIONAL ARGUMENTS:
location:
vector of location parameters. This is replicated to be the same length as p or q or the number of deviates generated. Missing values are not accepted.
scale:
vector of (positive) scale parameters. This is replicated to be the same length as p or q or the number of deviates generated. Missing values are not accepted.
VALUE:
density (dcauchy), probability (pcauchy), quantile (qcauchy), or random sample (rcauchy) for the cauchy distribution with parameters location and scale.
SIDE EFFECTS:
The function rcauchy causes creation of the dataset .Random.seed if it does not already exist, otherwise its value is updated.
DETAILS:
Elements of q or p that are missing will cause the corresponding elements of the result to be missing.
BACKGROUND:
The Cauchy is a real valued distribution symmetric about location, and has long enough tails that the expectation does not exist. The default distribution is the same as Student's t distribution with one degree of freedom (see T). The harmonic mean of variates that have positive density at 0 is typically distributed as Cauchy. The Cauchy also appears in the theory of Brownian motion.
REFERENCES:
Johnson, N. L. and Kotz, S. (1970). Continuous Univariate Distributions, vol. 1. Houghton-Mifflin, Boston.
SEE ALSO:
set.seed , Stable .
EXAMPLES: 
rcauchy(20,0,10) #sample of 20, location 0, scale 10