RelDists (version 1.0.0)

OW: The Odd Weibull family

Description

The function OW() defines the Odd Weibull distribution, a three parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss().

Usage

OW(mu.link = "log", sigma.link = "log", nu.link = "log")

Value

Returns a gamlss.family object which can be used to fit a OW 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.

nu.link

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

Author

Jaime Mosquera Gutiérrez

Details

The odd Weibull with parameters mu, sigma and nu has density given by

\(f(t) = \left( \frac{\sigma\nu}{t} \right) (\mu t)^\sigma e^{(\mu t)^\sigma} \left(e^{(\mu t)^{\sigma}}-1\right)^{\nu-1} \left[ 1 + \left(e^{(\mu t)^{\sigma}}-1\right)^\nu \right]^{-2}\)

for x > 0.

References

Cooray2006RelDists

Examples

# Example 1
# Generating some random values with
# known mu, sigma and nu
y <- rOW(n=200, mu=0.1, sigma=7, nu = 1.1)

# Fitting the model
require(gamlss)
mod <- gamlss(y~1, sigma.fo=~1, nu.fo=~1, family="OW",
              control=gamlss.control(n.cyc=500, 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 <- 500
x1 <- runif(n)
x2 <- runif(n)
x3 <- runif(n)
mu <- exp(1.2 + 2 * x1)
sigma <- 2.12 + 3 * x2
nu <- exp(0.2 - x3)
x <- rOW(n=n, mu, sigma, nu)

mod <- gamlss(x~x1, sigma.fo=~x2, nu.fo=~x3, 
              family=OW(sigma.link='identity'), 
              control=gamlss.control(n.cyc=300, trace=FALSE))

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