RelDists (version 1.0.0)

IW: The Inverse Weibull family

Description

The Inverse Weibull distribution

Usage

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

Value

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

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.

Author

Johan David Marin Benjumea,

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

almalki2014modificationsRelDists

drapella1993complementaryRelDists

See Also

dIW

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'))
exp(coef(mod, what='sigma'))

# 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")
coef(mod, what="sigma")