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)

Freddy Hernandez, [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=1, sigma=2)

# Fitting the model
require(gamlss)
mod <- gamlss(y~1, mu.fo=~1, sigma.fo=~1, family="IW")

# 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 <- 100
x1 <- runif(n)
x2 <- runif(n)
mu <- exp(2 + -1 * x1)
sigma <- exp(2 - 2 * x2)
y <- rIW(n=n, mu=mu, sigma=sigma)

mod <- gamlss(y~x1, mu.fo=~1, sigma.fo=~x2, family=IW)

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

# Example 3
# Using the dataset from Kundu and Howlader (2010) Bayesian inference and 
# prediction of the inverse Weibull distribution for Type-II censored data

y <- c(12, 15, 22, 24, 24, 32, 32, 33, 34, 38, 38, 43, 44, 48, 52, 
       53, 54, 54, 55, 56, 57, 58, 58, 59, 60, 60, 60, 60, 61, 62, 
       63, 65, 65, 67, 68, 70, 70, 72, 73, 75, 76, 76, 81, 83, 84, 
       85, 87, 91, 95, 96, 98, 99, 109, 110, 121, 127, 129, 131, 
       143, 146, 146, 175, 175, 211, 233, 258, 258, 263, 297, 341, 
       341, 376)

y <- y / 1000

mod <- gamlss(y~1, mu.fo=~1, sigma.fo=~1, family="IW",
              control=gamlss.control(n.cyc=5000, trace=FALSE))
exp(coef(mod, what="mu"))
exp(coef(mod, what="sigma"))

ousuga/RelDists documentation built on July 10, 2024, 12:48 p.m.