The Log-Weibull family

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.

Value

Returns a gamlss.family object which can be used to fit a LW distribution in the gamlss() function.

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.

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.

Author

Amylkar Urrea Montoya, amylkar.urrea@udea.edu.co

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')
#> (Intercept) 
#> -0.02913717 
exp(coef(mod, 'sigma'))
#> (Intercept) 
#>    1.554876 

# 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")
#> (Intercept)          x1 
#>    1.124928   -2.411863 
coef(mod, what="sigma")
#> (Intercept)          x2 
#>    1.916280   -3.129541