GGD: The Generalized Gompertz family

In ousuga/RelDists: Estimation for some Reliability Distributions

The Generalized Gompertz family

Description

The Generalized Gompertz family

Usage

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

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.

Details

The Generalized Gompertz Distribution with parameters mu, sigma and nu has density given by

f(x)= ν μ \exp(-\frac{μ}{σ}(\exp(σ x - 1))) (1 - \exp(-\frac{μ}{σ}(\exp(σ x - 1))))^{(ν - 1)} ,

for x ≥q 0, μ > 0, σ ≥q 0 and ν > 0

Value

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

Author(s)

Johan David Marin Benjumea, [e-mail]

References

\insertRef

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"))

ousuga/RelDists documentation built on Jan. 12, 2023, 10:27 p.m.