LO {gamlss.dist}

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)=\frac{1}{\sigma} e^{-\left(\frac{y-\mu}{\sigma}\right)} [1+e^{-\left(\frac{y-\mu}{\sigma}\right)}]^{-2}

for y=(-\infty,\infty), \mu=(-\infty,\infty) and \sigma>0, see page 368 of Rigby et al. (2019).

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/ \sqrt3 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, doi:10.1201/9780429298547. 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, doi:10.18637/jss.v023.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. doi:10.1201/b21973

(see also https://www.gamlss.com/).

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)