BGE function

The Beta Generalized Exponentiated family

BGE(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 BGE distribution in the gamlss() function.

Details

The Beta Generalized Exponentiated distribution with parameters mu, sigma, nu and tau has density given by

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

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

Examples

# Generating some random values with
# known mu, sigma, nu and tau
y <- rBGE(n=100, mu = 1.5, sigma =1.7, nu=1, tau=1)

# Fitting the model
require(gamlss)

mod <- gamlss(y~1, sigma.fo=~1, nu.fo=~1, tau.fo=~1, family=BGE,
              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(0.5 - x1)
sigma <- exp(0.8 - x2)
nu <- 1
tau <- 1
x <- rBGE(n=n, mu, sigma, nu, tau)

mod <- gamlss(x~x1, sigma.fo=~x2, nu.fo=~1, tau.fo=~1, family=BGE,
              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="barreto2010beta",package="RelDists")

See Also

dBGE

Author(s)

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