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)

Arguments

x,q vector of quantiles.
p vector of probabilities.
n number of observations to generate.
location,scale location and scale parameters.

Value

These functions provide information about the Cauchy distribution with location parameter location and scale parameter scale.

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

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.

See Also

dt for the t distribution which generalizes dcauchy(*, l = 0, s = 1).

Examples

dcauchy(-1:4) == 1 / (pi*(1 + (-1:4)^2))


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