KumIW | R Documentation |
The Kumaraswamy Inverse Weibull family
KumIW(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 Kumaraswamy Inverse Weibull Distribution with parameters mu
,
sigma
and nu
has density given by
f(x)= μ σ ν x^{-μ - 1} \exp{- σ x^{-μ}} (1 - \exp{- σ x^{-μ}})^{ν - 1},
for x > 0, μ > 0, σ > 0 and ν > 0.
Returns a gamlss.family object which can be used to fit a KumIW distribution in the gamlss()
function.
Johan David Marin Benjumea, johand.marin@udea.edu.co
almalki2014modificationsRelDists
\insertRefshahbaz2012kumaraswamyRelDists
dKumIW
# Example 1 # Generating some random values with # known mu, sigma, nu and tau y <- rKumIW(n=1000, mu = 1.5, sigma= 1.5, nu = 5) # Fitting the model require(gamlss) mod <- gamlss(y~1, sigma.fo=~1, nu.fo=~1, family='KumIW', 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, min=0.4, max=0.6) x2 <- runif(n, min=0.4, max=0.6) mu <- exp(1 - x1) sigma <- exp(1 - x2) nu <- 5 x <- rKumIW(n=n, mu, sigma, nu) mod <- gamlss(x~x1, sigma.fo=~x2, nu.fo=~1, family=KumIW, 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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