GMW {RelDists}

The Generalized Modified Weibull family

Description

The Generalized modified Weibull distribution

Usage

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

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 "sqrt" link as the default for the nu parameter.

tau.link

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

Details

The Generalized modified Weibull distribution with parameters mu, sigma, nu and tau has density given by

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

for x > 0.

Value

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

See Also

dGMW

Examples

# Example 1
# Generating some random values with
# known mu, sigma, nu and tau
y <- rGMW(n=100, mu=2, sigma=0.5, nu=2, tau=1.5)

# Fitting the model
require(gamlss)

mod <- gamlss(y~1, sigma.fo=~1, nu.fo=~1, tau.fo=~ 1, family='GMW',
              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'))
(coef(mod, what='nu'))^2
(coef(mod, what='tau'))^2

# Example 2
# Generating random values under some model
## Not run: 
n <- 1000
x1 <- runif(n)
x2 <- runif(n)
mu <- exp(2 + -3 * x1)
sigma <- exp(3 - 2 * x2)
nu <- 2
tau <- 1.5
x <- rGMW(n=n, mu, sigma, nu, tau)

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

coef(mod, what="mu")
coef(mod, what="sigma")
coef(mod, what="nu")^2
coef(mod, what="tau")^2

## End(Not run)