RelDists (version 1.0.0)

LW: The Log-Weibull family

Description

The Log-Weibull distribution

Usage

LW(mu.link = "identity", sigma.link = "log")

Value

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

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.

Author

Amylkar Urrea Montoya,

Details

The Log-Weibull Distribution with parameters mu and sigma has density given by

\(f(y)=(1/\sigma) e^{((y - \mu)/\sigma)} exp\{-e^{((y - \mu)/\sigma)}\},\)

for - infty < y < infty.

References

almalki2014modificationsRelDists

Gumbel1958RelDists

See Also

dLW

Examples

# Example 1
# Generating some random values with
# known mu and sigma 
y <- rLW(n=100, mu=0, sigma=1.5)

# Fitting the model
require(gamlss)

mod <- gamlss(y~1, sigma.fo=~1, family= 'LW',
              control=gamlss.control(n.cyc=5000, trace=FALSE))

# Extracting the fitted values for mu and sigma
# using the inverse link function
coef(mod, 'mu')
exp(coef(mod, 'sigma'))

# 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 <- 1.5 - 3 * x1
sigma <- exp(1.4 - 2 * x2)
x <- rLW(n=n, mu, sigma)

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

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