WG function

The Weibull Geometric family

The Weibull Geometric distribution

WG(mu.link = "log", sigma.link = "log", nu.link = "logit")

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 WG distribution in the gamlss() function.

Details

The weibull geometric distribution with parameters mu, sigma and nu has density given by

c("f(x) = (\\sigma \\mu^\\sigma (1-\\nu) x^(\\sigma - 1) \\exp(-(\\mu x)^\\sigma)) \n", "(1- \\nu \\exp(-(\\mu x)^\\sigma))^{-2},")

for $x > 0$, $\mu > 0$, $\sigma > 0$ and $0 < \nu < 1$.

Examples

# Example 1
# Generating some random values with
# known mu, sigma and nu
y <- rWG(n=100,  mu = 0.9, sigma = 2, nu = 0.5)

# Fitting the model
require(gamlss)

mod <- gamlss(y~1, sigma.fo=~1, nu.fo=~1, family='WG',
              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(- 0.2 * x1)
sigma <- exp(1.2 - 1 * x2)
nu    <- 0.5
x     <- rWG(n=n, mu, sigma, nu)

mod <- gamlss(x~x1, mu.fo=~x1, sigma.fo=~x2, nu.fo=~1, family=WG,
              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="barreto2011weibull",package="RelDists")

See Also

dWG

Author(s)

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