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

Almalki, S. J., & Nadarajah, S. (2014). Modifications of the Weibull distribution: A review. Reliability Engineering & System Safety, 124, 32-55.

De Gusmao, F. R., Ortega, E. M., & Cordeiro, G. M. (2011). The generalized inverse Weibull distribution. Statistical Papers, 52, 591-619.

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) 
#>    2.856589 
exp(coef(mod, what='sigma'))
#> (Intercept) 
#>     4.95933 
exp(coef(mod, what='nu'))
#> (Intercept) 
#>   0.6515828 

# 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 
#>  -0.9507364   2.7995149 
coef(mod, what="sigma")
#> (Intercept)          x2 
#>    1.482412   -1.540473 
exp(coef(mod, what="nu"))
#> (Intercept) 
#>   0.5268569