RelDists (version 1.0.0)

KumIW: The Kumaraswamy Inverse Weibull family

Description

The Kumaraswamy Inverse Weibull family

Usage

KumIW(mu.link = "log", sigma.link = "log", nu.link = "log")

Value

Returns a gamlss.family object which can be used to fit a KumIW 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.

nu.link

defines the nu.link, with "log" link as the default for the nu parameter.

Author

Johan David Marin Benjumea,

Details

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

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

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

References

almalki2014modificationsRelDists

shahbaz2012kumaraswamyRelDists

See Also

dKumIW

Examples

# Example 1
# Generating some random values with
# known mu, sigma, nu and tau
y <- rKumIW(n=1000, mu = 1.5, sigma=  1.5, nu = 5)

# 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, min=0.4, max=0.6)
x2 <- runif(n, min=0.4, max=0.6)
mu <- exp(1 - x1)
sigma <- exp(1 - x2)
nu <- 5
x <- rKumIW(n=n, mu, sigma, nu)

mod <- gamlss(x~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"))