AddW {RelDists}

The Additive Weibull family

Description

The Additive Weibull distribution

Usage

AddW(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

Additive Weibull distribution with parameters mu, sigma, nu and tau has density given by

f(x) = (\mu\nu x^{\nu - 1} + \sigma\tau x^{\tau - 1}) \exp({-\mu x^{\nu} - \sigma x^{\tau} }),

for x > 0.

Value

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

Author(s)

Amylkar Urrea Montoya, [e-mail]

References

Almalki SJ, Nadarajah S (2014). “Modifications of the Weibull distribution: A review.” Reliability Engineering & System Safety, 124, 32–55. doi:10.1016/j.ress.2013.11.010.

Xie M, Lai CD (1996). “Reliability analysis using an additive Weibull model with bathtub-shaped failure rate function.” Reliability Engineering and System Safety, 52, 83–93. doi:10.1016/0951-8320(95)00149-2.

See Also

dAddW

Examples

# Example 1
# Generating some random values with
# known mu, sigma, nu and tau
# Will not be run this example because high number is cycles
# is needed in order to get good estimates
## Not run: 
y <- rAddW(n=100, mu=1.5, sigma=0.2, nu=3, tau=0.8)

# Fitting the model
require(gamlss)

mod <- gamlss(y~1, sigma.fo=~1, nu.fo=~1, tau.fo=~1, family='AddW',
              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'))

## 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 <- runif(n, min=0.4, max=0.6)
x2 <- runif(n, min=0.4, max=0.6)
mu <- exp(1.67 + -3 * x1)
sigma <- exp(0.69 - 2 * x2)
nu <- 3
tau <- 0.8
x <- rAddW(n=n, mu, sigma, nu, tau)

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

## End(Not run)