R: Logistic distribution for fitting a GAMLSS

LO {gamlss.dist} | R Documentation

## 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

    LO(mu.link = "identity", sigma.link = "log")
    dLO(x, mu = 0, sigma = 1, log = FALSE)
    pLO(q, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE)
    qLO(p, mu = 0, sigma = 1, lower.tail = TRUE, log.p = FALSE)
    rLO(n, mu = 0, sigma = 1)

### Arguments

`mu.link` | Defines the `mu.link`, with "identity" link as the default for the mu parameter
`sigma.link` | Defines the `sigma.link`, with "log" link as the default for the sigma parameter
`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 `length(n) > 1`, the length is taken to be the number required

### 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, 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.

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 https://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, https://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.

### See Also

`gamlss.family`, `NO`, `TF`

### Examples

    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)

[Package gamlss.dist version 5.3-2 Index]