WEI3 can be used to define the Weibull distribution, a two parameter distribution, for a
gamlss.family object to be used in GAMLSS fitting using the function gamlss().
This is a parameterization of the Weibull distribution where $\mu$ is the mean of the distribution.
[Note that the GAMLSS functions WEI and WEI2 use
different parameterizations for fitting the Weibull distribution.]
The functions dWEI3, pWEI3, qWEI3 and rWEI3 define the density, distribution function, quantile function and random
generation for the specific parameterization of the Weibull distribution.WEI3(mu.link = "log", sigma.link = "log")
dWEI3(x, mu = 1, sigma = 1, log = FALSE)
pWEI3(q, mu = 1, sigma = 1, lower.tail = TRUE, log.p = FALSE)
qWEI3(p, mu = 1, sigma = 1, lower.tail = TRUE, log.p = FALSE)
rWEI3(n, mu = 1, sigma = 1)mu.link, with "log" link as the default for the mu parameter, other links are "inverse" and "identity"sigma.link, with "log" link as the default for the sigma parameter, other link is the "inverse" and "identity"length(n) > 1, the length is
taken to be the number requiredWEI3() returns a gamlss.family object which can be used to fit a Weibull distribution in the gamlss() function.
dWEI3() gives the density, pWEI3() gives the distribution
function, qWEI3() gives the quantile function, and rWEI3()
generates random deviates. The latest functions are based on the equivalent R functions for Weibull distribution.WEI3 the estimated parameters mu and sigma can be highly correlated so it is advisable to use the
CG() method for fitting [as the RS() method can be very slow in this situation.]WEI3 is given by
$$f(y|\mu,\sigma)= \frac{\sigma}{\beta} \left(\frac{y}{\beta}\right)^{\sigma-1} e^{-\left(\frac{y}{\beta}\right)^{\sigma}}$$
where $\beta=\frac{\mu}{\Gamma((1/\sigma)+1)}$ for $y>0$, $\mu>0$ and $\sigma>0$.
The GAMLSS functions dWEI3, pWEI3, qWEI3, and rWEI3 can be used to provide the pdf, the cdf, the quantiles and
random generated numbers for the Weibull distribution with argument mu, and sigma.
[See the GAMLSS function WEI for a different parameterization of the Weibull.]gamlss.family, WEI, WEI2WEI3()
dat<-rWEI(100, mu=.1, sigma=2)
# library(gamlss)
# gamlss(dat~1, family=WEI3, method=CG())Run the code above in your browser using DataLab