GammaW | R Documentation |
The Gamma Weibull family
GammaW(mu.link = "log", sigma.link = "log", nu.link = "log")
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. |
The Gamma Weibull distribution with parameters mu
,
sigma
and nu
has density given by
f(x)= \frac{σ μ^{ν}}{Γ (ν)} x^{ν σ - 1} \exp(-μ x^σ),
for x > 0, μ > 0, σ ≥q 0 and ν > 0.
Returns a gamlss.family object which can be used to fit a GammaW distribution in the gamlss()
function.
Johan David Marin Benjumea, johand.marin@udea.edu.co
almalki2014modificationsRelDists
\insertRefstacy1962generalizationRelDists
dGammaW
# Example 1 # Generating some random values with # known mu, sigma and nu y <- rGammaW(n=100, mu = 0.5, sigma = 2, nu=1) # Fitting the model require(gamlss) mod <- gamlss(y~1, sigma.fo=~1, nu.fo=~1, family='GammaW', 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 <- 200 x1 <- runif(n) x2 <- runif(n) mu <- exp(-1.6 * x1) sigma <- exp(1.1 - 1 * x2) nu <- 1 x <- rGammaW(n=n, mu, sigma, nu) mod <- gamlss(x~x1, mu.fo=~x1, sigma.fo=~x2, nu.fo=~1, family=GammaW, control=gamlss.control(n.cyc=50000, trace=FALSE)) coef(mod, what="mu") coef(mod, what="sigma") coef(mod, what='nu')
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