The Reflected Weibull family

Reflected Weibull distribution

Usage

RW(mu.link = "log", sigma.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.

Value

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

Details

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

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

for y < 0

References

Almalki, S. J., & Nadarajah, S. (2014). Modifications of the Weibull distribution: A review. Reliability Engineering & System Safety, 124, 32-55.

Cohen, A. C. (1973). The reflected Weibull distribution. Technometrics, 15(4), 867-873.

Author

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

Examples

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

# Fitting the model
require(gamlss)

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

# Extracting the fitted values for mu and sigma
# using the inverse link function
exp(coef(mod, 'mu'))
#> (Intercept) 
#>   0.8147178 
exp(coef(mod, 'sigma'))
#> (Intercept) 
#>    1.002485 

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

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

coef(mod, what="mu")
#> (Intercept)          x1 
#>    1.359454   -1.239177 
coef(mod, what="sigma")
#> (Intercept)          x2 
#>    2.148321   -2.240320