# Waring distribution for fitting a GAMLSS model

### Description

The function `WARING()`

defines the Waring distribution, a two parameter
distribution, for a `gamlss.family`

object to be used in GAMLSS fitting
using the function `gamlss()`

, with mean equal to the parameter `mu`

and scale parameter `sigma`

. The functions `dWARING`

, `pWARING`

, `qWARING`

and `rWARING`

define the density, distribution function, quantile function and random generation for the `WARING`

parameterization of the Waring distribution.

### Usage

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### Arguments

`mu.link` |
Defines the |

`sigma.link` |
Defines the |

`x` |
vector of (non-negative integer) quantiles. |

`q` |
vector of quantiles. |

`p` |
vector of probabilities. |

`n` |
number of random values to return. |

`mu` |
vector of positive |

`sigma` |
vector of positive |

`lower.tail` |
logical; if |

`log, log.p` |
logical; if |

`max.value` |
constant; generates a sequence of values for the cdf function. |

### Details

The Waring distribution has density,

*f(y|mu, sigma)= ((1+sigma) Gamma(y+mu/sigma) Gamma((mu+sigma+1)/sigma))/(sigma Gamma(y+(mu+1)/sigma+2) Gamma(mu/sigma))*

for *y=0,1,2,…*, *mu>0* and *sigma>0*.

### Value

Returns a `gamlss.family`

object which can be used to fit a Waring distribution in the `gamlss()`

function.

### Author(s)

Fiona McElduff, Bob Rigby and Mikis Stasinopoulos. f.mcelduff@ich.ucl.ac.uk

### References

Wimmer, G. and Altmann, G. (1999) *Thesaurus of univariate discrete probability distributions.* Stamm.

### See Also

`gamlss.family`

### Examples

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