EMWEx function

The Exponentiated Modifien Weibull Extension family

EMWEx(mu.link = "log", sigma.link = "log", nu.link = "log", tau.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.
• tau.link: defines the tau.link, with "log" link as the default for the tau parameter.

Returns

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

Details

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

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

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

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"))

References

Rdpack::insert_ref(key="almalki2014modifications",package="RelDists")

Rdpack::insert_ref(key="sarhan2013exponentiated",package="RelDists")

See Also

dEMWEx

Author(s)

Johan David Marin Benjumea, johand.marin@udea.edu.co