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.

Value

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

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 \(\nu > 0\).

References

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

Author

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

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'))
#> (Intercept) 
#>    5.042591 
exp(coef(mod, what='sigma'))
#> (Intercept) 
#>   0.4851037 
exp(coef(mod, what='nu'))
#> (Intercept) 
#>   0.9337674 

# 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")
#> (Intercept)          x1 
#>    5.365488   -5.927616 
coef(mod, what="sigma")
#> (Intercept)          x2 
#>    1.051958   -2.326782 
exp(coef(mod, what="nu"))
#> (Intercept) 
#>    1.097681