RelDists (version 1.0.0)

GGD: The Generalized Gompertz family

Description

The Generalized Gompertz family

Usage

GGD(mu.link = "log", sigma.link = "log", nu.link = "log")

Value

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

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.

Author

Johan David Marin Benjumea,

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

el2013generalizedRelDists

See Also

dGGD

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'))
exp(coef(mod, what='sigma'))
exp(coef(mod, what='nu'))

# 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")
coef(mod, what="sigma")
exp(coef(mod, what="nu"))