The Weigted Generalized Exponential-Exponential family
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.
- nu.link
defines the nu.link, with "log" link as the default for the nu parameter.
Value
Returns a gamlss.family object which can be used to fit a WGEE distribution in the gamlss() function.
Details
The Weigted Generalized Exponential-Exponential distribution with parameters mu,
sigma and nu has density given by
\(f(x)= \sigma \nu \exp(-\nu x) (1 - \exp(-\nu x))^{\sigma - 1} (1 - \exp(-\mu \nu x)) / 1 - \sigma B(\mu + 1, \sigma),\)
for \(x > 0\), \(\mu > 0\), \(\sigma > 0\) and \(\nu > 0\).
References
Mahdavi A (2015). “Two weighted distributions generated by exponential distribution.” Journal of Mathematical Extension, 9, 1--12.
Author
Johan David Marin Benjumea, johand.marin@udea.edu.co
Examples
# Example 1
# Generating some random values with
# known mu, sigma and nu
y <- rWGEE(n=1000, mu = 5, sigma = 0.5, nu = 1)
# Fitting the model
require(gamlss)
mod <- gamlss(y~1, sigma.fo=~1, nu.fo=~1, family='WGEE',
control=gamlss.control(n.cyc=5000, trace=FALSE))
# Extracting the fitted values for mu, sigma and nu
# using the inverse link function
exp(coef(mod, what='mu'))
#> (Intercept)
#> 6.534813
exp(coef(mod, what='sigma'))
#> (Intercept)
#> 0.7095732
exp(coef(mod, what='nu'))
#> (Intercept)
#> 1.066985
# Example 2
# Generating random values under some model
n <- 500
x1 <- runif(n, min=0.4, max=0.6)
x2 <- runif(n, min=0.4, max=0.6)
mu <- exp(2 - x1)
sigma <- exp(1 - 3*x2)
nu <- 1
x <- rWGEE(n=n, mu, sigma, nu)
mod <- gamlss(x~x1, sigma.fo=~x2, nu.fo=~1, family=WGEE,
control=gamlss.control(n.cyc=50000, trace=FALSE))
coef(mod, what="mu")
#> (Intercept) x1
#> 1.627308 2.478713
coef(mod, what="sigma")
#> (Intercept) x2
#> 0.758560 -1.380891
exp(coef(mod, what="nu"))
#> (Intercept)
#> 1.106103