KumIW: The Kumaraswamy Inverse Weibull family

In ousuga/RelDists: Estimation for some Reliability Distributions

The Kumaraswamy Inverse Weibull family

Description

The Kumaraswamy Inverse Weibull family

Usage

KumIW(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.

Details

The Kumaraswamy Inverse Weibull Distribution with parameters mu, sigma and nu has density given by

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

for x > 0, \mu > 0, \sigma > 0 and \nu > 0.

The KumIW distribution with \nu=1 corresponds with the IW distribution.

Value

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

Author(s)

Freddy Hernandez, [e-mail]

References

\insertRef

almalki2014modificationsRelDists

\insertRef

shahbaz2012kumaraswamyRelDists

See Also

dKumIW

Examples

# Example 1
# Generating some random values with
# known mu, sigma and nu
y <- rKumIW(n=100, mu=1.5, sigma=2.3, nu=1)

# Fitting the model
require(gamlss)

mod <- gamlss(y~1, sigma.fo=~1, nu.fo=~1, family=KumIW,
              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"))
exp(coef(mod, what="nu"))

# Example 2
# Generating random values under some model
n <- 200
x1 <- runif(n)
x2 <- runif(n)
mu <- exp(1 +  -1 * x1)
sigma <- exp(1 + -1 * x2)
nu <- 5
y <- rKumIW(n=n, mu=mu, sigma=sigma, nu=nu)

mod <- gamlss(y~x1, sigma.fo=~x2, nu.fo=~1, family=KumIW,
              control=gamlss.control(n.cyc=5000, trace=FALSE))

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

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