Description Usage Arguments Details Value Note Author(s) References See Also Examples

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()

1 2 3 4 5 |

`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 |

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*.

`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.

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

Mikis Stasinopoulos, Bob Rigby and Calliope Akantziliotou

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.

Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC. An older version can be found in http://www.gamlss.com/.

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.

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017)
*Flexible Regression and Smoothing: Using GAMLSS in R*, Chapman and Hall/CRC.

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)
``` |

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