MOK | R Documentation |
The Marshall-Olkin Kappa family
MOK(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 Marshall-Olkin Kappa distribution with parameters mu
,
sigma
, nu
and tau
has density given by
f(x)=\frac{τ\frac{μν}{σ}≤ft(\frac{x}{σ}\right)^{ν-1} ≤ft(μ+≤ft(\frac{x}{σ}\right)^{μν}\right)^{-\frac{μ+1}{μ}}}{≤ft(τ+(1-τ)≤ft(\frac{≤ft(\frac{x}{σ}\right)^{μν}}{μ+≤ft(\frac{x}{σ}\right)^{μν}}\right)^{\frac{1}{μ}}\right)^2}
for x > 0.
Returns a gamlss.family object which can be used to fit a MOK distribution in the gamlss()
function.
Johan David Marin Benjumea, johand.marin@udea.edu.co
javed2018marshallRelDists
dMOK
# Example 1 # Generating some random values with # known mu, sigma, nu and tau y <- rMOK(n=100, mu = 1, sigma = 3.5, nu = 3, tau = 2) # Fitting the model require(gamlss) mod <- gamlss(y~1, sigma.fo=~1, nu.fo=~1, tau.fo=~1, family=MOK, 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 <- rMOK(n=n, mu, sigma, nu, tau) mod <- gamlss(x~x1, sigma.fo=~x2, nu.fo=~1, tau.fo=~1, family=MOK, 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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