# Logistic distribution for fitting a GAMLSS

### Description

The function `LO()`

, or equivalently `Logistic()`

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

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

### Usage

1 2 3 4 5 |

### Arguments

`mu.link` |
Defines the |

`sigma.link` |
Defines the |

`x,q` |
vector of quantiles |

`mu` |
vector of location parameter values |

`sigma` |
vector of scale parameter values |

`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] |

`p` |
vector of probabilities. |

`n` |
number of observations. If |

### Details

Definition file for Logistic distribution.

*f(y|mu,sigma)=(1/sigma)*exp((y-mu)/sigma)*((1+exp(-(y-mu)/sigma))^(-2))*

for *y=(-Inf,+Inf)*, *μ=(-Inf,+Inf)* and *σ>0*.

### Value

`LO()`

returns a `gamlss.family`

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

function.
`dLO()`

gives the density, `pLO()`

gives the distribution
function, `qLO()`

gives the quantile function, and `rLO()`

generates random deviates for the logistic distribution.
The latest functions are based on the equivalent `R`

functions for logistic distribution.

### Note

*mu* is the mean and *sigma*pi/sqrt(3)* is the standard deviation for the logistic distribution

### Author(s)

Mikis Stasinopoulos mikis.stasinopoulos@gamlss.org, Bob Rigby and Calliope Akantziliotou

### References

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion),
*Appl. Statist.*, **54**, part 3, pp 507-554.

Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R.
*Journal of Statistical Software*, Vol. **23**, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07.

### See Also

`gamlss.family`

, `NO`

, `TF`

### Examples

1 2 3 4 5 6 7 8 | ```
LO()# gives information about the default links for the Logistic distribution
plot(function(y) dLO(y, mu=10 ,sigma=2), 0, 20)
plot(function(y) pLO(y, mu=10 ,sigma=2), 0, 20)
plot(function(y) qLO(y, mu=10 ,sigma=2), 0, 1)
# library(gamlss)
# data(abdom)
# h<-gamlss(y~cs(x,df=3), sigma.formula=~cs(x,1), family=LO, data=abdom) # fits
# plot(h)
``` |