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The Additive Weibull family

Source: R/AddW.R
AddW.Rd

The Additive Weibull distribution

Usage

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

Arguments

defines the mu.link, with "log" link as the default for the mu parameter.

defines the sigma.link, with "log" link as the default for the sigma.

defines the nu.link, with "log" link as the default for the nu parameter.

defines the tau.link, with "log" link as the default for the tau parameter.

Value

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

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.

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

Author

Amylkar Urrea Montoya, amylkar.urrea@udea.edu.co

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
if (FALSE) { # \dontrun{
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'))
} # }

# 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
if (FALSE) { # \dontrun{
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"))
} # }