QXGP | R Documentation |
The Quasi XGamma Poisson family
QXGP(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 Quasi XGamma Poisson distribution with parameters mu
,
sigma
and nu
has density given by
f(x)= K(μ, σ, ν)(\frac {σ^{2} x^{2}}{2} + μ) exp(\frac{ν exp(-σ x)(1 + μ + σ x + \frac {σ^{2}x^{2}}{2})}{1+μ} - σ x),
for x > 0, μ> 0, σ> 0, ν> 1.
where
K(μ, σ, ν) = \frac{ν σ}{(exp(ν)-1)(1+μ)}
Returns a gamlss.family object which can be used to fit a QXGP distribution in the gamlss()
function.
Amylkar Urrea Montoya, amylkar.urrea@udea.edu.co
subhradev2018RelDists
dQXGP
# Example 1 # Generating some random values with # known mu, sigma and nu y <- rQXGP(n=200, mu=4, sigma=2, nu=3) # Fitting the model require(gamlss) mod <- gamlss(y~1, sigma.fo=~1, nu.fo=~1, family='QXGP', 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(-2.19 + 3 * x1) sigma <- exp(1 - 2 * x2) nu <- 1 x <- rQXGP(n=n, mu, sigma, nu) mod <- gamlss(x~x1, sigma.fo=~x2, nu.fo=~1, family=QXGP, 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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