MW: The Modified Weibull family

In ousuga/RelDists: Estimation for some Reliability Distributions

The Modified Weibull family

Description

#' The Modified Weibull distribution

Usage

MW(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 Modified Weibull distribution with parameters mu, sigma and nu has density given by

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

for x > 0, μ > 0, σ ≥q 0 and ν ≥q 0.

Value

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

Author(s)

Johan David Marin Benjumea, [e-mail]

References

\insertRef

almalki2014modificationsRelDists

\insertRef

lai2003modifiedRelDists

See Also

dMW

Examples

# Example 1
# Generating some random values with
# known mu, sigma and nu
y <- rMW(n=100, mu = 2, sigma = 1.5, nu = 0.2)

# Fitting the model
require(gamlss)

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

# Example 2
# Generating random values under some model
n     <- 200
x1    <- rpois(n, lambda=2)
x2    <- runif(n)
mu    <- exp(3 -1 * x1)
sigma <- exp(2 - 2 * x2)
nu    <- 0.2
x     <- rMW(n=n, mu, sigma, nu)

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

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

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