MOK: The Marshall-Olkin Kappa family

In RelDists: Estimation for some Reliability Distributions

The Marshall-Olkin Kappa family

Description

The Marshall-Olkin Kappa family

Usage

MOK(mu.link = "log", sigma.link = "log", nu.link = "log", tau.link = "log")

Arguments

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.

Details

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.

Value

Returns a gamlss.family object which can be used to fit a MOK distribution in the gamlss() function.

Author(s)

Johan David Marin Benjumea, [e-mail]

References

\insertRef

javed2018marshallRelDists

See Also

dMOK

Examples

# 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"))

RelDists documentation built on Dec. 23, 2022, 1:26 a.m.