FWE function

The Flexible Weibull Extension family

The function FWE() defines the Flexible Weibull distribution, a two parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss().

FWE(mu.link = "log", 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.

Returns

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

Details

The Flexible Weibull extension with parameters mu and sigma

has density given by

$f(x) = (\mu + \sigma/x^2) exp(\mu x - \sigma/x) exp(-exp(\mu x-\sigma/x))$

for x>0.

Examples

# Example 1
# Generating some random values with
# known mu and sigma
y <- rFWE(n=100, mu=0.75, sigma=1.3)

# Fitting the model
require(gamlss)
mod <- gamlss(y~1, sigma.fo=~1, family='FWE',
              control=gamlss.control(n.cyc=5000, trace=FALSE))

# Extracting the fitted values for mu and sigma
# using the inverse link function
exp(coef(mod, what='mu'))
exp(coef(mod, what='sigma'))

# Example 2
# Generating random values under some model
n <- 200
x1 <- runif(n)
x2 <- runif(n)
mu <- exp(1.21 - 3 * x1)
sigma <- exp(1.26 - 2 * x2)
x <- rFWE(n=n, mu, sigma)

mod <- gamlss(x~x1, sigma.fo=~x2, family=FWE, 
              control=gamlss.control(n.cyc=5000, trace=FALSE))

coef(mod, what="mu")
coef(mod, what="sigma")