# Skew-Cauchy Distribution

### Description

Density function, distribution function, quantiles and random number generation for the skew-Cauchy (SC) distribution.

### Usage

1 2 3 4 |

### Arguments

`x` |
vector of quantiles. Missing values ( |

`p` |
vector of probabilities. Missing values ( |

`xi` |
vector of location parameters. |

`omega` |
vector of (positive) scale parameters. |

`alpha` |
vector of slant parameters. |

`dp` |
a vector of length 3 whose elements represent the parameters
described above. If |

`n` |
sample size. |

`log` |
logical flag used in |

### Value

density (`dsc`

), probability (`psc`

), quantile (`qsc`

)
or random sample (`rsc`

) from the skew-Cauchy distribution with given
`xi`

, `omega`

and `alpha`

parameters or from the extended
skew-normal if `tau!=0`

### Details

Typical usages are

1 2 3 4 5 6 7 8 |

### Background

The skew-Cauchy distribution can be thought as a skew-*t* with tail-weight
parameter `nu=1`

. In this case, closed-form expressions of the
distribution function and the quantile function have been obtained by
Behboodian *et al.* (2006).
The key facts are summarized in Complement 4.2 of Azzalini and Capitanio (2014).
A multivariate version of the distribution exists.

### References

Azzalini, A. with the collaboration of Capitanio, A. (2014).
*The Skew-normal and Related Families*.
Cambridge University Press, IMS Monographs series.

Behboodian, J., Jamalizadeh, A., and Balakrishnan, N. (2006).
A new class of skew-Cauchy distributions.
*Statist. Probab. Lett.* **76**, 1488–1493.

### See Also

`dst`

, `dmsc`

### Examples

1 2 3 4 5 |