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The Flexible Weibull Extension family

Source: R/FWE.R
FWE.Rd

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

defines the mu.link, with "log" link as the default for the mu parameter.

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 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")
#> GAMLSS-RS iteration 1: Global Deviance = 143.188 
#> GAMLSS-RS iteration 2: Global Deviance = 142.9185 
#> GAMLSS-RS iteration 3: Global Deviance = 142.8914 
#> GAMLSS-RS iteration 4: Global Deviance = 142.888 
#> GAMLSS-RS iteration 5: Global Deviance = 142.8875 

# Extracting the fitted values for mu and sigma
# using the inverse link function
exp(coef(mod, what="mu"))
#> (Intercept) 
#>   0.8663081 
exp(coef(mod, what="sigma"))
#> (Intercept) 
#>    1.558488 

# 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)
y <- rFWE(n=n, mu=mu, sigma=sigma)

mod <- gamlss(y~x1, sigma.fo=~x2, family=FWE)
#> GAMLSS-RS iteration 1: Global Deviance = 2522.512 
#> GAMLSS-RS iteration 2: Global Deviance = 1393.345 
#> GAMLSS-RS iteration 3: Global Deviance = 631.842 
#> GAMLSS-RS iteration 4: Global Deviance = 308.8378 
#> GAMLSS-RS iteration 5: Global Deviance = 308.3761 
#> GAMLSS-RS iteration 6: Global Deviance = 308.3006 
#> GAMLSS-RS iteration 7: Global Deviance = 308.2873 
#> GAMLSS-RS iteration 8: Global Deviance = 308.285 
#> GAMLSS-RS iteration 9: Global Deviance = 308.2846 

coef(mod, what="mu")
#> (Intercept)          x1 
#>    1.253865   -3.050367 
coef(mod, what="sigma")
#> (Intercept)          x2 
#>    1.254222   -2.057288