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.

Value

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

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.

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 .

Author

Amylkar Urrea Montoya, amylkar.urrea@udea.edu.co

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'))
#> (Intercept) 
#>    2.776996 
exp(coef(mod, what='sigma'))
#> (Intercept) 
#>    5.747789 
exp(coef(mod, what='nu'))
#> (Intercept) 
#>   0.6439106 

# 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")
#> (Intercept)          x1 
#>   -1.071631    2.929594 
coef(mod, what="sigma")
#> (Intercept)          x2 
#>    1.642404   -1.869564 
exp(coef(mod, what="nu"))
#> (Intercept) 
#>   0.5757264