EGG: The four parameter Exponentiated Generalized Gamma family

In ousuga/RelDists: Estimation for some Reliability Distributions

The four parameter Exponentiated Generalized Gamma family

Description

The four parameter Exponentiated Generalized Gamma distribution

Usage

EGG(mu.link = "log", sigma.link = "log", nu.link = "log", tau.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.
tau.link	defines the tau.link, with "log" link as the default for the tau parameter.

Details

Four parameter Exponentiated Generalized Gamma distribution with parameters mu, sigma, nu and tau has density given by

f(x) = \frac{\nu \sigma}{\mu \Gamma(\tau)} \left(\frac{x}{\mu}\right)^{\sigma \tau -1} \exp\left\{ - \left( \frac{x}{\mu} \right)^\sigma \right\} \left\{ \gamma_1\left( \tau, \left( \frac{x}{\mu} \right)^\sigma \right) \right\}^{\nu-1} ,

for x > 0.

Value

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

Author(s)

Amylkar Urrea Montoya, [e-mail]

References

Almalki, S. J., & Nadarajah, S. (2014). Modifications of the Weibull distribution: A review. Reliability Engineering & System Safety, 124, 32-55.

Cordeiro, G. M., Ortega, E. M., & Silva, G. O. (2011). The exponentiated generalized gamma distribution with application to lifetime data. Journal of statistical computation and simulation, 81(7), 827-842.

See Also

dEGG

Examples

# Example 1
# Generating some random values with
# known mu, sigma, nu and tau

set.seed(123456)
y <- rEGG(n=100, mu=0.1, sigma=0.8, nu=10, tau=1.5)

# Fitting the model
require(gamlss)

mod <- gamlss(y~1, sigma.fo=~1, nu.fo=~1, tau.fo=~1, 
              family=EGG,
              control=gamlss.control(n.cyc=500, trace=FALSE))

# Extracting the fitted values for mu, sigma, nu and tau
# using the inverse link function
exp(coef(mod, what="mu"))
exp(coef(mod, what="sigma"))
exp(coef(mod, what="nu"))
exp(coef(mod, what="tau"))


# Example 2
# Generating random values under some model


# A function to simulate a data set with Y ~ EGG
gendat <- function(n) {
  x1 <- runif(n)
  x2 <- runif(n)
  mu    <- exp(-0.8 + -3 * x1)
  sigma <- exp(0.77 - 2 * x2)
  nu    <- 10
  tau   <- 1.5
  y <- rEGG(n=n, mu=mu, sigma=sigma, nu=nu, tau)
  data.frame(y=y, x1=x1, x2=x2)
}

set.seed(12345)
dat <- gendat(n=200)

mod <- gamlss(y~x1, sigma.fo=~x2, nu.fo=~1, tau.fo=~1, 
              family=EGG, data=dat,
              control=gamlss.control(n.cyc=500, trace=FALSE))

coef(mod, what="mu")
coef(mod, what="sigma")
exp(coef(mod, what="nu"))
exp(coef(mod, what="tau"))

ousuga/RelDists documentation built on July 4, 2025, 10:55 a.m.