The Weibull Geometric distribution
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 WG distribution in the gamlss() function.
Details
The weibull geometric distribution with parameters mu,
sigma and nu has density given by
\(f(x) = (\sigma \mu^\sigma (1-\nu) x^(\sigma - 1) \exp(-(\mu x)^\sigma)) (1- \nu \exp(-(\mu x)^\sigma))^{-2},\)
for \(x > 0\), \(\mu > 0\), \(\sigma > 0\) and \(0 < \nu < 1\).
References
Barreto-Souza W, de Morais AL, Cordeiro GM (2011). “The Weibull-geometric distribution.” Journal of Statistical Computation and Simulation, 81(5), 645--657.
Author
Johan David Marin Benjumea, johand.marin@udea.edu.co
Examples
# Example 1
# Generating some random values with
# known mu, sigma and nu
y <- rWG(n=100, mu = 0.9, sigma = 2, nu = 0.5)
# Fitting the model
require(gamlss)
mod <- gamlss(y~1, sigma.fo=~1, nu.fo=~1, family='WG',
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)
#> 1.800367
exp(coef(mod, what='sigma'))
#> (Intercept)
#> 0.9776491
exp(coef(mod, what='nu'))
#> (Intercept)
#> 1.15513
# Example 2
# Generating random values under some model
n <- 200
x1 <- runif(n)
x2 <- runif(n)
mu <- exp(- 0.2 * x1)
sigma <- exp(1.2 - 1 * x2)
nu <- 0.5
x <- rWG(n=n, mu, sigma, nu)
mod <- gamlss(x~x1, mu.fo=~x1, sigma.fo=~x2, nu.fo=~1, family=WG,
control=gamlss.control(n.cyc=50000, trace=FALSE))
coef(mod, what="mu")
#> (Intercept) x1
#> 0.7996677 -0.3305537
coef(mod, what="sigma")
#> (Intercept) x2
#> -0.08631752 0.28309339
coef(mod, what='nu')
#> (Intercept)
#> 0.4456102