EGG {RelDists} | R Documentation |
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, amylkar.urrea@udea.edu.co
References
Almalki SJ, Nadarajah S (2014). “Modifications of the Weibull distribution: A review.” Reliability Engineering & System Safety, 124, 32–55. doi:10.1016/j.ress.2013.11.010.
Gauss M. C, Edwin M.M O, Giovana O. S (2011). “The exponentiated generalized gamma distribution with application to lifetime data.” Journal of Statistical Computation and Simulation, 81(7), 827–842. doi:10.1080/00949650903517874.
See Also
Examples
# Example 1
# Generating some random values with
# known mu, sigma, nu and tau
y <- rEGG(n=500, 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
n <- 200
x1 <- runif(n, min=0.2, max=0.8)
x2 <- runif(n, min=0.2, max=0.8)
mu <- exp(-0.8 + -3 * x1)
sigma <- exp(0.77 - 2 * x2)
nu <- 10
tau <- 1.5
y <- rEGG(n=n, mu, sigma, nu, tau)
mod <- gamlss(y~x1, sigma.fo=~x2, nu.fo=~1, tau.fo=~1, family=EGG,
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"))