EMWEx: The Exponentiated Modifien Weibull Extension family

In ousuga/RelDists: Estimation for some Reliability Distributions

The Exponentiated Modifien Weibull Extension family

Description

The Exponentiated Modifien Weibull Extension family

Usage

EMWEx(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 Beta-Weibull distribution with parameters mu, sigma, nu and tau has density given by

f(x)= ν σ τ (\frac{x}{μ})^{σ-1} \exp((\frac{x}{μ})^σ + ν μ (1- \exp((\frac{x}{μ})^σ))) (1 - \exp (νμ (1- \exp((\frac{x}{μ})^σ))))^{τ-1} ,

for x > 0, ν> 0, μ > 0, σ> 0 and τ > 0.

Value

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

Author(s)

Johan David Marin Benjumea, [e-mail]

References

\insertRef

almalki2014modificationsRelDists

\insertRef

sarhan2013exponentiatedRelDists

See Also

dEMWEx

Examples

# Example 1
# Generating some random values with
# known mu, sigma, nu and tau
y <- rEMWEx(n=100, mu = 1, sigma =1.21, nu=1, tau=2)

# Fitting the model
require(gamlss)

mod <- gamlss(y~1, sigma.fo=~1, nu.fo=~1, tau.fo=~1, family=EMWEx,
              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(0.75 - x1)
sigma <- exp(0.5 - x2)
nu <- 1
tau <- 2
x <- rEMWEx(n=n, mu, sigma, nu, tau)

mod <- gamlss(x~x1, sigma.fo=~x2, nu.fo=~1, tau.fo=~1, family=EMWEx,
              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"))

ousuga/RelDists documentation built on Jan. 12, 2023, 10:27 p.m.