The Generalized Gompertz 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 GGD distribution in the gamlss() function.
.
Details
The Generalized Gompertz Distribution with parameters mu,
sigma and nu has density given by
\(f(x)= \nu \mu \exp(-\frac{\mu}{\sigma}(\exp(\sigma x - 1))) (1 - \exp(-\frac{\mu}{\sigma}(\exp(\sigma x - 1))))^{(\nu - 1)} ,\)
for \(x \geq 0\), \(\mu > 0\), \(\sigma \geq 0\) and \(\nu > 0\)
References
El-Gohary A, Alshamrani A, Al-Otaibi AN (2013). “The generalized Gompertz distribution.” Applied Mathematical Modelling, 37(1-2), 13--24.
Author
Johan David Marin Benjumea, johand.marin@udea.edu.co
Examples
#Example 1
# Generating some random values with
# known mu, sigma, nu and tau
y <- rGGD(n=1000, mu=1, sigma=0.3, nu=1.5)
# Fitting the model
require(gamlss)
mod <- gamlss(y~1, sigma.fo=~1, nu.fo=~1, family='GGD',
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)
#> 1.071621
exp(coef(mod, what='sigma'))
#> (Intercept)
#> 0.2736874
exp(coef(mod, what='nu'))
#> (Intercept)
#> 1.6616
# Example 2
# Generating random values under some model
n <- 200
x1 <- runif(n, min=0.4, max=0.6)
x2 <- runif(n, min=0.4, max=0.6)
mu <- exp(0.5 - x1)
sigma <- exp(-1 - x2)
nu <- 1.5
x <- rGGD(n=n, mu, sigma, nu)
mod <- gamlss(x~x1, sigma.fo=~x2, nu.fo=~1, family=GGD,
control=gamlss.control(n.cyc=5000, trace=FALSE))
coef(mod, what="mu")
#> (Intercept) x1
#> 0.899877 -2.144417
coef(mod, what="sigma")
#> (Intercept) x2
#> -2.422859 2.969301
exp(coef(mod, what="nu"))
#> (Intercept)
#> 1.279496