ExW | R Documentation |
The Extended Weibull family
ExW(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 Extended Weibull distribution with parameters mu
,
sigma
and nu
has density given by
f(x) = \frac{μ σ ν x^{σ -1} exp({-μ x^{σ}})} {[1 -(1-ν) exp({-μ x^{σ}})]^2},
for x > 0.
Returns a gamlss.family object which can be used to fit a ExW distribution in the gamlss()
function.
Amylkar Urrea Montoya, amylkar.urrea@udea.edu.co
almalki2014modificationsRelDists
\insertRefZhang2007RelDists
dExW
# Example 1 # Generating some random values with # known mu, sigma and nu y <- rExW(n=200, mu=0.3, sigma=2, nu=0.05) # Fitting the model require(gamlss) mod <- gamlss(y~1, sigma.fo=~1, nu.fo=~1, family='ExW', 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 + 3 * x1) sigma <- exp(1.3 - 2 * x2) nu <- 0.05 x <- rExW(n=n, mu, sigma, nu) mod <- gamlss(x~x1, sigma.fo=~x2, nu.fo=~1, family=ExW, control=gamlss.control(n.cyc=5000, trace=FALSE)) coef(mod, what="mu") coef(mod, what="sigma") exp(coef(mod, what="nu"))
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