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().
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 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'))
#> (Intercept)
#> 0.7902188
exp(coef(mod, what='sigma'))
#> (Intercept)
#> 1.561474
# 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")
#> (Intercept) x1
#> 1.259052 -3.128705
coef(mod, what="sigma")
#> (Intercept) x2
#> 1.265880 -2.198918