GammaW {RelDists}

The Gamma Weibull family

Description

The Gamma Weibull family

Usage

GammaW(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 Gamma Weibull distribution with parameters mu, sigma and nu has density given by

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

for x > 0, \mu > 0, \sigma \geq 0 and \nu > 0.

Value

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

Author(s)

Johan David Marin Benjumea, [e-mail]

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.

Stacy EW, others (1962). “A generalization of the gamma distribution.” The Annals of mathematical statistics, 33(3), 1187–1192.

See Also

dGammaW

Examples

# Example 1
# Generating some random values with
# known mu, sigma and nu
y <- rGammaW(n=100, mu = 0.5, sigma = 2, nu=1)

# Fitting the model
require(gamlss)

mod <- gamlss(y~1, sigma.fo=~1, nu.fo=~1, family='GammaW',
              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)
x2    <- runif(n)
mu    <- exp(-1.6 * x1)
sigma <- exp(1.1 - 1 * x2)
nu    <- 1
x     <- rGammaW(n=n, mu, sigma, nu)

mod <- gamlss(x~x1, mu.fo=~x1, sigma.fo=~x2, nu.fo=~1, family=GammaW,
              control=gamlss.control(n.cyc=50000, trace=FALSE))

coef(mod, what="mu")
coef(mod, what="sigma")
coef(mod, what='nu')