WP | R Documentation |
The Weibull Poisson family
WP(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 Weibull Poisson distribution with parameters mu
,
sigma
and nu
has density given by
f(x) = \frac{μ σ ν e^{-ν}} {1-e^{-ν}} x^{μ-1} exp({-σ x^{μ}+ν exp({-σ} x^{μ}) }),
for x > 0.
Returns a gamlss.family object which can be used to fit a WP distribution in the gamlss()
function.
Amylkar Urrea Montoya, amylkar.urrea@udea.edu.co
almalki2014modificationsRelDists
\insertRefWanbo2012RelDists
dWP
# Example 1 # Generating some random values with # known mu, sigma and nu y <- rWP(n=300, mu=1.5, sigma=0.5, nu=0.5) # Fitting the model require(gamlss) mod <- gamlss(y~1, sigma.fo=~1, nu.fo=~1, family='WP', 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 <- 2000 x1 <- runif(n, min=0.4, max=0.6) x2 <- runif(n, min=0.4, max=0.6) mu <- exp(-1.3 + 3 * x1) sigma <- exp(0.69 - 2 * x2) nu <- 0.5 x <- rWP(n=n, mu, sigma, nu) mod <- gamlss(x~x1, sigma.fo=~x2, nu.fo=~1, family=WP, 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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