EOFNH | R Documentation |
The Extended Odd Frechet-Nadarjad-Hanhighi family
EOFNH(mu.link = "log", sigma.link = "log", nu.link = "log", tau.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. |
tau.link |
defines the tau.link, with "log" link as the default for the tau parameter. |
The Extended Odd Frechet-Nadarjad-Hanhighi distribution with parameters mu
,
sigma
, nu
and tau
has density given by
f(x)= \frac{μσντ(1+ν x)^{σ-1}e^{(1-(1+ν x)^σ)}[1-(1-e^{(1-(1+ν x)^σ)})^{μ}]^{τ-1}}{(1-e^{(1-(1+ν x)^{σ})})^{μτ+1}} e^{-[(1-e^{(1-(1+ν x)^σ)})^{-μ}-1]^{τ}},
for x > 0, μ > 0, σ > 0, ν > 0 and τ > 0.
Returns a gamlss.family object which can be used to fit a EOFNH distribution in the gamlss()
function.
Johan David Marin Benjumea, johand.marin@udea.edu.co
nasiru2018extendedRelDists
dEOFNH
# Example 1 # Generating some random values with # known mu, sigma, nu and tau y <- rEOFNH(n=100, mu=1, sigma=2.1, nu=0.8, tau=1) # Fitting the model require(gamlss) mod <- gamlss(y~1, sigma.fo=~1, nu.fo=~1, tau.fo=~1, family=EOFNH, control=gamlss.control(n.cyc=5000, trace=FALSE)) # Extracting the fitted values for mu, sigma, nu and tau # using the inverse link function exp(coef(mod, what='mu')) exp(coef(mod, what='sigma')) exp(coef(mod, what='nu')) exp(coef(mod, what='tau')) # 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(0.5 + x1) sigma <- exp(0.8 + x2) nu <- 1 tau <- 0.5 x <- rEOFNH(n=n, mu, sigma, nu, tau) mod <- gamlss(x~x1, sigma.fo=~x2, nu.fo=~1, tau.fo=~1, family=EOFNH, control=gamlss.control(n.cyc=5000, trace=FALSE)) coef(mod, what="mu") coef(mod, what="sigma") exp(coef(mod, what="nu")) exp(coef(mod, what="tau"))
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