# Yule distribution for fitting a GAMLSS model

### Description

The function `YULE`

defines the Yule distribution, a one parameter
distribution, for a `gamlss.family`

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

, with mean equal to the parameter `mu`

.
The functions `dYULE`

, `pYULE`

, `qYULE`

and `rYULE`

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

parameterization of the Yule distribution.

### Usage

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### Arguments

`mu.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 |

`lower.tail` |
logical; if |

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

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

### Details

The Yule distribution has density

*p(y)=beta(lambda+1, x+1)/beta(lambda, 1)*

where

*lambda = (mu+1)/mu*

for *y=0,1,2,…* and *mu>0*.

### Value

Returns a `gamlss.family`

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

function.

### Author(s)

Fiona McElduff, Bob Rigby and Mikis Stasinopoulos.

### References

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

### See Also

`gamlss.family`

### Examples

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