The Inverse Weibull family

The Inverse Weibull distribution

Usage

IW(mu.link = "log", sigma.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.

Value

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

Details

The Inverse Weibull distribution with parameters mu, sigma has density given by

\(f(x) = \mu \sigma x^{-\sigma-1} \exp(\mu x^{-\sigma})\)

for \(x > 0\), \(\mu > 0\) and \(\sigma > 0\)

References

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

Drapella, A. (1993). The complementary Weibull distribution: unknown or just forgotten?. Quality and reliability engineering international, 9(4), 383-385.

Author

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

Examples

# Example 1
# Generating some random values with
# known mu and sigma
y <- rIW(n=100, mu=5, sigma=2.5)

# Fitting the model
require(gamlss)

mod <- gamlss(y~1, mu.fo=~1, sigma.fo=~1, family='IW',
              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) 
#>    4.030121 
exp(coef(mod, what='sigma'))
#> (Intercept) 
#>    2.375744 

# Example 2
# Generating random values under some model
n <- 200
x1 <- rpois(n, lambda=2)
x2 <- runif(n)
mu <- exp(2 + -1 * x1)
sigma <- exp(2 - 2 * x2)
x <- rIW(n=n, mu, sigma)

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

coef(mod, what="mu")
#> (Intercept)          x1 
#>    2.311472   -1.155356 
coef(mod, what="sigma")
#> (Intercept)          x2 
#>    1.974543   -1.855939