Cauchy {stats} | R Documentation |

## The Cauchy Distribution

### Description

Density, distribution function, quantile function and random
generation for the Cauchy distribution with location parameter
`location`

and scale parameter `scale`

.

### Usage

dcauchy(x, location = 0, scale = 1, log = FALSE)
pcauchy(q, location = 0, scale = 1, lower.tail = TRUE, log.p = FALSE)
qcauchy(p, location = 0, scale = 1, lower.tail = TRUE, log.p = FALSE)
rcauchy(n, location = 0, scale = 1)

### Arguments

`x, q` |
vector of quantiles. |

`p` |
vector of probabilities. |

`n` |
number of observations. If `length(n) > 1` , the length
is taken to be the number required. |

`location, scale` |
location and scale parameters. |

`log, log.p` |
logical; if TRUE, probabilities p are given as log(p). |

`lower.tail` |
logical; if TRUE (default), probabilities are
*P[X <= x]*, otherwise, *P[X > x]*. |

### Details

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*.

### Value

`dcauchy`

, `pcauchy`

, and `qcauchy`

are respectively
the density, distribution function and quantile function of the Cauchy
distribution. `rcauchy`

generates random deviates from the
Cauchy.

### Source

`dcauchy`

, `pcauchy`

and `qcauchy`

are all calculated
from numerically stable versions of the definitions.

`rcauchy`

uses inversion.

### References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988)
*The New S Language*.
Wadsworth & Brooks/Cole.

Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995)
*Continuous Univariate Distributions*, volume 1, chapter 16.
Wiley, New York.

### See Also

`dt`

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

.

### Examples

dcauchy(-1:4)

[Package

*stats* version 2.5.0

Index]