GammaW function

The Gamma Weibull family

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.

Returns

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

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 $\nu > 0$.

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')

References

Rdpack::insert_ref(key="almalki2014modifications",package="RelDists")

Rdpack::insert_ref(key="stacy1962generalization",package="RelDists")

See Also

dGammaW

Author(s)

Johan David Marin Benjumea, johand.marin@udea.edu.co