GIW {RelDists}

The Generalized Inverse Weibull family

Description

The Generalized Inverse Weibull family

Usage

GIW(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 Generalized Inverse Weibull distribution with parameters mu, sigma and nu has density given by

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

for x > 0.

Value

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

Author(s)

Amylkar Urrea Montoya, [e-mail]

References

Felipe R SdG, Edwin M MO, Gauss M C (2009). “The generalized inverse Weibull distribution.” Statistical papers, 52(3), 591–619. doi:10.1007/s00362-009-0271-3.

See Also

dGIW

Examples

# Example 1
# Generating some random values with
# known mu, sigma and nu
y <- rGIW(n=200, mu=3, sigma=5, nu=0.5)

# Fitting the model
require(gamlss)

mod <- gamlss(y~1, sigma.fo=~1, nu.fo=~1, family='GIW',
              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 <- 500
x1 <- runif(n, min=0.4, max=0.6)
x2 <- runif(n, min=0.4, max=0.6)
mu <- exp(-1.02 + 3 * x1)
sigma <- exp(1.69 - 2 * x2)
nu <- 0.5
x <- rGIW(n=n, mu, sigma, nu)

mod <- gamlss(x~x1, sigma.fo=~x2, nu.fo=~1, family=GIW,
              control=gamlss.control(n.cyc=5000, trace=FALSE))

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