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The four parameter Exponentiated Generalized Gamma family

Source: R/EGG.R
EGG.Rd

The four parameter Exponentiated Generalized Gamma distribution

Usage

EGG(mu.link = "log", sigma.link = "log", nu.link = "log", tau.link = "log")

Arguments

defines the mu.link, with "log" link as the default for the mu parameter.

defines the sigma.link, with "log" link as the default for the sigma.

defines the nu.link, with "log" link as the default for the nu parameter.

defines the tau.link, with "log" link as the default for the tau parameter.

Value

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

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.

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

dEGG

Author

Amylkar Urrea Montoya, amylkar.urrea@udea.edu.co

Examples

# Example 1
# Generating some random values with
# known mu, sigma, nu and tau
# \donttest{
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))
#> Warning: Algorithm RS has not yet converged

# Extracting the fitted values for mu, sigma, nu and tau
# using the inverse link function
exp(coef(mod, what='mu'))
#> (Intercept) 
#>   0.1660713 
exp(coef(mod, what='sigma'))
#> (Intercept) 
#>    0.870753 
exp(coef(mod, what='nu'))
#> (Intercept) 
#>    68.20416 
exp(coef(mod, what='tau'))
#> (Intercept) 
#>   0.2628551 
# }

# Example 2
# Generating random values under some model
# \donttest{
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")
#> (Intercept)          x1 
#>  -0.9269798  -2.9740746 
coef(mod, what="sigma")
#> (Intercept)          x2 
#>   0.6640167  -1.9576499 
exp(coef(mod, what="nu"))
#> (Intercept) 
#>     45.3087 
exp(coef(mod, what="tau"))
#> (Intercept) 
#>   0.7043806 
# }