EW: The Exponentiated Weibull family

In ousuga/RelDists: Estimation for some Reliability Distributions

The Exponentiated Weibull family

Description

The Exponentiated Weibull distribution

Usage

EW(mu.link = "log", sigma.link = "log", nu.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.

Details

The Exponentiated Weibull Distribution with parameters mu, sigma and nu has density given by

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

for x > 0.

Value

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

See Also

dEW

Examples

# Example 1
# Generating some random values with
# known mu, sigma and nu
# Will not be run this example because high number is cycles
# is needed in order to get good estimates
## Not run: 
y <- rEW(n=100, mu=2, sigma=1.5, nu=0.5)

# Fitting the model
require(gamlss)
mod <- gamlss(y~1, sigma.fo=~1, nu.fo=~1, family='EW',
              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'))

## End(Not run)

# Example 2
# Generating random values under some model
# Will not be run this example because high number is cycles
# is needed in order to get good estimates
## Not run: 
n <- 200
x1 <- rpois(n, lambda=2)
x2 <- runif(n)
mu <- exp(2 + -3 * x1)
sigma <- exp(3 - 2 * x2)
nu <- 2
x <- rEW(n=n, mu, sigma, nu)

mod <- gamlss(x~x1, sigma.fo=~x2, nu.fo=~1, family=EW, 
              control=gamlss.control(n.cyc=5000, trace=FALSE))

coef(mod, what="mu")
coef(mod, what="sigma")
exp(coef(mod, what="nu"))

## End(Not run)

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