RelDists (version 1.0.0)

EMWEx: The Exponentiated Modifien Weibull Extension family

Description

The Exponentiated Modifien Weibull Extension family

Usage

EMWEx(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 EMWEx 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

Johan David Marin Benjumea,

Details

The Beta-Weibull distribution with parameters mu, sigma, nu and tau has density given by

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

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

References

almalki2014modificationsRelDists

sarhan2013exponentiatedRelDists

See Also

dEMWEx

Examples

# Example 1
# Generating some random values with
# known mu, sigma, nu and tau
y <- rEMWEx(n=100, mu = 1, sigma =1.21, nu=1, tau=2)

# Fitting the model
require(gamlss)

mod <- gamlss(y~1, sigma.fo=~1, nu.fo=~1, tau.fo=~1, family=EMWEx,
              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
n <- 200
x1 <- runif(n, min=0.4, max=0.6)
x2 <- runif(n, min=0.4, max=0.6)
mu <- exp(0.75 - x1)
sigma <- exp(0.5 - x2)
nu <- 1
tau <- 2
x <- rEMWEx(n=n, mu, sigma, nu, tau)

mod <- gamlss(x~x1, sigma.fo=~x2, nu.fo=~1, tau.fo=~1, family=EMWEx,
              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"))