The Marshall-Olkin Extended Inverse Weibull family

Usage

MOEIW(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.

Value

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

Details

The Marshall-Olkin Extended Inverse Weibull distribution with parameters mu, sigma and nu has density given by

\(f(x) = \frac{\mu \sigma \nu x^{-(\sigma + 1)} exp\{{-\mu x^{-\sigma}}\}}{\{\nu -(\nu-1) exp\{{-\mu x ^{-\sigma}}\} \}^{2}},\)

for x > 0.

References

Hassan M O, A.H E, A.M.K T, Abdulkareem M Bc (2017). “Extended inverse Weibull distribution with reliability application.” Journal of the Egyptian Mathematical Society, 25, 343--349. doi:10.1016/j.joems.2017.02.006 , http://dx.doi.org/10.1016/j.joems.2017.02.006.

Author

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

Examples

# Example 1
# Generating some random values with
# known mu, sigma and nu
y <- rMOEIW(n=400, mu=0.6, sigma=1.7, nu=0.3)

# Fitting the model
require(gamlss)

mod <- gamlss(y~1, sigma.fo=~1, nu.fo=~1, family='MOEIW',
              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'))
#> (Intercept) 
#>   0.3561482 
exp(coef(mod, what='sigma'))
#> (Intercept) 
#>    2.038929 
exp(coef(mod, what='nu'))
#> (Intercept) 
#>    0.544687 

# Example 2
# Generating random values under some model
n <- 400
x1 <- runif(n, min=0.4, max=0.6)
x2 <- runif(n, min=0.4, max=0.6)
mu <- exp(-2.02 + 3 * x1)
sigma <- exp(2.23 - 2 * x2)
nu <- 0.3
x <- rMOEIW(n=n, mu, sigma, nu)

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

coef(mod, what="mu")
#> (Intercept)          x1 
#>   -1.925765    2.557897 
coef(mod, what="sigma")
#> (Intercept)          x2 
#>    2.486056   -2.504715 
exp(coef(mod, what="nu"))
#> (Intercept) 
#>   0.4007935