FWE {RelDists}

The Flexible Weibull Extension family

Description

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().

Usage

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.

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.

Value

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

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")