The Extended Exponential Geometric family

Usage

EEG(mu.link = "log", sigma.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.

Value

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

Details

The Extended Exponential Geometric distribution with parameters mu and sigma has density given by

\(f(x)= \mu \sigma \exp(-\mu x)(1 - (1 - \sigma)\exp(-\mu x))^{-2},\)

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

References

Almalki SJ, Nadarajah S (2014). “Modifications of the Weibull distribution: A review.” Reliability Engineering & System Safety, 124, 32–55. doi:10.1016/j.ress.2013.11.010 .

Adamidis K, Dimitrakopoulou T, Loukas S (2005). “On an extension of the exponential-geometric distribution.” Statistics & probability letters, 73(3), 259–269.

Author

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

Examples

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

# Fitting the model
require(gamlss)

mod <- gamlss(y~1, sigma.fo=~1, family=EEG,
              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'))
#> (Intercept) 
#>    0.814895 
exp(coef(mod, what='sigma'))
#> (Intercept) 
#>    1.418915 

# Example 2
# Generating random values under some model
n <- 200
x1 <- runif(n, min=0.1, max=0.2)
x2 <- runif(n, min=0.1, max=0.15)
mu <- exp(0.75 - x1)
sigma <- exp(0.5 - x2)
x <- rEEG(n=n, mu, sigma)

mod <- gamlss(x~x1, sigma.fo=~x2, family=EEG,
              control=gamlss.control(n.cyc=5000, trace=FALSE))

coef(mod, what="mu")
#> (Intercept)          x1 
#>   0.4961979  -0.7919087 
coef(mod, what="sigma")
#> (Intercept)          x2 
#>   0.5301076  -1.6138227