WP: The Weibull Poisson family

In ousuga/RelDists: Estimation for some Reliability Distributions

The Weibull Poisson family

Description

The Weibull Poisson family

Usage

WP(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 Weibull Poisson distribution with parameters mu, sigma and nu has density given by

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

for x > 0.

Value

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

Author(s)

Amylkar Urrea Montoya, [e-mail]

References

Lu, Wanbo, and Daimin Shi. "A new compounding life distribution: the Weibull–Poisson distribution." Journal of applied statistics 39.1 (2012): 21-38.

See Also

dWP

Examples

# Example 1
# Generating some random values with
# known mu, sigma and nu
y <- rWP(n=3000, mu=1.5, sigma=0.5, nu=0.5)

# Fitting the model
require(gamlss)

mod1 <- gamlss(y~1, sigma.fo=~1, nu.fo=~1, family=WP,
              control=gamlss.control(n.cyc=5000, trace=FALSE))

# Extracting the fitted values for mu, sigma and nu
# using the inverse link function
exp(coef(mod1, what="mu"))
exp(coef(mod1, what="sigma"))
exp(coef(mod1, what="nu"))

# Example 2
# Generating random values for a regression model

# A function to simulate a data set with Y ~ WP
gendat <- function(n) {
  x1 <- runif(n)
  x2 <- runif(n)
  mu <- exp(-1.3 + 3.1 * x1)
  sigma <- exp(0.9 - 3.2 * x2)
  nu <- 0.5
  y <- rWP(n=n, mu, sigma, nu)
  data.frame(y=y, x1=x1, x2)
}

set.seed(1234)
dat <- gendat(n=100)

# Fitting the model
mod2 <- NULL
mod2 <- gamlss(y~x1, sigma.fo=~x2, nu.fo=~1, 
               family=WP, data=dat,
              control=gamlss.control(n.cyc=5000, trace=FALSE))

coef(mod2, what="mu")
coef(mod2, what="sigma")
exp(coef(mod2, what="nu"))

ousuga/RelDists documentation built on March 29, 2025, 4:07 a.m.