WGEE {RelDists}

The Weigted Generalized Exponential-Exponential family

Description

The Weigted Generalized Exponential-Exponential family

Usage

WGEE(mu.link = "log", sigma.link = "log", nu.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.

Details

The Weigted Generalized Exponential-Exponential distribution with parameters mu, sigma and nu has density given by

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

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

Value

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

Author(s)

Johan David Marin Benjumea, [e-mail]

References

Mahdavi A (2015). “Two weighted distributions generated by exponential distribution.” Journal of Mathematical Extension, 9, 1–12.

See Also

dWGEE

Examples

# Example 1
# Generating some random values with
# known mu, sigma and  nu 
y <- rWGEE(n=1000, mu = 5, sigma = 0.5, nu = 1)

# Fitting the model
require(gamlss)

mod <- gamlss(y~1, sigma.fo=~1, nu.fo=~1, family='WGEE',
              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'))
exp(coef(mod, what='nu'))

# Example 2
# Generating random values under some model
n <- 500
x1 <- runif(n, min=0.4, max=0.6)
x2 <- runif(n, min=0.4, max=0.6)
mu <- exp(2 - x1)
sigma <- exp(1 - 3*x2)
nu <- 1
x <- rWGEE(n=n, mu, sigma, nu)

mod <- gamlss(x~x1, sigma.fo=~x2, nu.fo=~1, family=WGEE,
              control=gamlss.control(n.cyc=50000, trace=FALSE))

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