cauchy

The Cauchy distribution is an unbounded continuous distribution that has a sharp central peak but significantly broad tails. The tails are much heavier than the tails of the Normal distribution.

The Cauchy distribution can be used to represent the ratio of two equally distributed parameters in certain cases, e.g. the ratio of two normal parameters. This distribution has no finite moments because of its extensive tails. Thus it can also be used to generate wildly divergent data a long as the data has a central tendency.

Sample 

lambda =1; theta = 0

cauchy(double lambda, double theta)

Description

Generates a sample of the Cauchy distribution.

Parameters

Name Type Description
lambda double the scale parameter > 0
theta double the mode, or central peak position

Result

Type Description
double the generated sample
cauchy(double lambda)

Description

Generates a sample of the Cauchy distribution with theta set to 0. Is equivalent to cauchy(lambda, 0).

Parameters

Name Type Description
lambda double  the scale parameter > 0

Result

Type Description
double the generated sample

cauchy(double lambda, double theta, java.util.Random r)

Description

Generates a sample of the Cauchy distribution using the specified random number generator.

Parameters

Name Type Description
lambda double the scale parameter > 0
theta double the mode, or central peak position
r java.util.Random  the random number generator

Result

Type Description
double the generated sample