IW: The Inverse Weibull family

In ousuga/RelDists: Estimation for some Reliability Distributions

The Inverse Weibull family

Description

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.

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

Value

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

Author(s)

Johan David Marin Benjumea, [e-mail]

References

\insertRef

almalki2014modificationsRelDists

\insertRef

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")

ousuga/RelDists documentation built on March 29, 2025, 4:07 a.m.