LW {RelDists} | R Documentation |
The Log-Weibull family
Description
The Log-Weibull distribution
Usage
LW(mu.link = "identity", sigma.link = "log")
Arguments
mu.link |
defines the mu.link, with "log" link as the default for the mu parameter. |
sigma.link |
defines the sigma.link, with "log" link as the default for the sigma. |
Details
The Log-Weibull Distribution with parameters mu
and sigma
has density given by
f(y)=(1/\sigma) e^{((y - \mu)/\sigma)} exp\{-e^{((y - \mu)/\sigma)}\},
for - infty
< y < infty
.
Value
Returns a gamlss.family object which can be used to fit a LW distribution in the gamlss()
function.
Author(s)
Amylkar Urrea Montoya, amylkar.urrea@udea.edu.co
References
Almalki SJ, Nadarajah S (2014). “Modifications of the Weibull distribution: A review.” Reliability Engineering & System Safety, 124, 32–55. doi:10.1016/j.ress.2013.11.010.
E.J G (1958). Statistics of extremes. Columbia University Press. ISBN 10:0231021909.
See Also
Examples
# Example 1
# Generating some random values with
# known mu and sigma
y <- rLW(n=100, mu=0, sigma=1.5)
# Fitting the model
require(gamlss)
mod <- gamlss(y~1, sigma.fo=~1, family= 'LW',
control=gamlss.control(n.cyc=5000, trace=FALSE))
# Extracting the fitted values for mu and sigma
# using the inverse link function
coef(mod, 'mu')
exp(coef(mod, 'sigma'))
# Example 2
# Generating random values under some model
n <- 200
x1 <- runif(n, min=0.4, max=0.6)
x2 <- runif(n, min=0.4, max=0.6)
mu <- 1.5 - 3 * x1
sigma <- exp(1.4 - 2 * x2)
x <- rLW(n=n, mu, sigma)
mod <- gamlss(x~x1, sigma.fo=~x2, family=LW,
control=gamlss.control(n.cyc=5000, trace=FALSE))
coef(mod, what="mu")
coef(mod, what="sigma")