Cauchy Distribution

DESCRIPTION:

Density, cumulative probability, quantiles and random generation of the Cauchy distribution.

USAGE:

dcauchy(x, location=0, scale=1, log=F) 
pcauchy(q, location=0, scale=1) 
qcauchy(p, location=0, scale=1) 
rcauchy(n, location=0, scale=1, bigdata=F) 

REQUIRED ARGUMENTS:

x
vector or bdVector of quantiles. Missing values ( NAs) are allowed.
q
vector or bdVector of quantiles. Missing values ( NAs) are allowed.
p
vector or bdVector 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 or bdVector 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 or bdVector 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.
bigdata
a logical value; if TRUE, an object of type bdVector is returned. Otherwise, a vector object is returned. This argument can be used only if the bigdata library section has been loaded.
log
a logical scalar; if TRUE, dcauchy will return the log of the density, not the density itself.

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.

For details on the uniform random number generator implemented in S-PLUS, see the set.seed help file.

REFERENCES:

Johnson, N. L. and Kotz, S. (1970). Continuous Univariate Distributions, vol. 1. Houghton-Mifflin, Boston.

SEE ALSO:

, .

EXAMPLES:

rcauchy(20,0,10) #sample of 20, location 0, scale 10