The four parameter Exponentiated Generalized Gamma family

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.

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 .

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) 
#>   0.1717804 
exp(coef(mod, what='sigma'))
#> (Intercept) 
#>   0.8820903 
exp(coef(mod, what='nu'))
#> (Intercept) 
#>    70.08323 
exp(coef(mod, what='tau'))
#> (Intercept) 
#>   0.2613447 
# }

# 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 
#>  -0.5275907  -3.0078615 
coef(mod, what="sigma")
#> (Intercept)          x2 
#>    1.038302   -2.538644 
exp(coef(mod, what="nu"))
#> (Intercept) 
#>    13.04321 
exp(coef(mod, what="tau"))
#> (Intercept) 
#>   0.9509624 
# }