Rev Language Reference

dnCauchy - Cauchy Distribution

The Cauchy distribution describes the distribution of the ratio of two independent normal variables with mean 0 and variance 1.

Aliases

  • dnLorentz

Usage

dnCauchy(Real location, RealPos scale)

Arguments

location : Real (pass by const reference)
The location parameter.
scale : RealPos (pass by const reference)
The scale parameter.

Domain Type

Real

Details

The Cauchy distribution takes two parameters, location and scale. It is a symmetric distribution, but its tails are broad enough that it has no defined mean or variance. The probability density function is f(x) = 1/(pi * scale) * 1 / (1 + x - (location/scale)^2)

Example

# we simulate some obversations
x <- rCauchy(n=10,location=0,scale=1)
# let's see what the mean and the variance are.
The mean will not converge with more samples, the Cauchy family has no moments.
mean(x)
var(x)
sd(x)

See Also

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