RelDists (version 1.0.0)

AddW: The Additive Weibull family

Description

The Additive Weibull distribution

Usage

AddW(mu.link = "log", sigma.link = "log", nu.link = "log", tau.link = "log")

Value

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

tau.link

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

Author

Amylkar Urrea Montoya,

Details

Additive Weibull distribution with parameters mu, sigma, nu and tau has density given by

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

for x > 0.

References

almalki2014modificationsRelDists

Xie1996RelDists

See Also

dAddW

Examples

# Example 1
# Generating some random values with
# known mu, sigma, nu and tau
# Will not be run this example because high number is cycles
# is needed in order to get good estimates
if (FALSE) {
y <- rAddW(n=100, mu=1.5, sigma=0.2, nu=3, tau=0.8)

# Fitting the model
require(gamlss)

mod <- gamlss(y~1, sigma.fo=~1, nu.fo=~1, tau.fo=~1, family='AddW',
              control=gamlss.control(n.cyc=5000, trace=FALSE))

# Extracting the fitted values for mu, sigma, nu and tau
# using the inverse link function
exp(coef(mod, what='mu'))
exp(coef(mod, what='sigma'))
exp(coef(mod, what='nu'))
exp(coef(mod, what='tau'))
}

# Example 2
# Generating random values under some model
# Will not be run this example because high number is cycles
# is needed in order to get good estimates
if (FALSE) {
n <- 200
x1 <- runif(n, min=0.4, max=0.6)
x2 <- runif(n, min=0.4, max=0.6)
mu <- exp(1.67 + -3 * x1)
sigma <- exp(0.69 - 2 * x2)
nu <- 3
tau <- 0.8
x <- rAddW(n=n, mu, sigma, nu, tau)

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

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