WEI 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(). [Note that the GAMLSS function WEI2 uses a
different parameterization for fitting the Weibull distribution.]
The functions dWEI, pWEI, qWEI and rWEI define the density, distribution function, quantile function and random
generation for the specific parameterization of the Weibul distribution.WEI(mu.link = "log", sigma.link = "log")
dWEI(x, mu = 1, sigma = 1, log = FALSE)
pWEI(q, mu = 1, sigma = 1, lower.tail = TRUE, log.p = FALSE)
qWEI(p, mu = 1, sigma = 1, lower.tail = TRUE, log.p = FALSE)
rWEI(n, mu = 1, sigma = 1)mu.link, with "log" link as the default for the mu parameter, other links are "inverse", "identity" and "own"sigma.link, with "log" link as the default for the sigma parameter, other link is the "inverse", "identity" and "own"length(n) > 1, the length is
taken to be the number requiredWEI() returns a gamlss.family object which can be used to fit a Weibull distribution in the gamlss() function.
dWEI() gives the density, pWEI() gives the distribution
function, qWEI() gives the quantile function, and rWEI()
generates random deviates. The latest functions are based on the equivalent R functions for Weibull distribution.WEI is given by
$$f(y|\mu,\sigma)=\frac{\sigma y^{\sigma-1}}{\mu^\sigma}
\hspace{1mm} \exp \left[ -\left(\frac{y }{\mu}\right)^{\sigma}
\right]$$
for $y>0$, $\mu>0$ and $\sigma>0$.
The GAMLSS functions dWEI, pWEI, qWEI, and rWEI 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 WEI2 for a different parameterization of the Weibull.]gamlss.family, WEI2, WEI3WEI()
dat<-rWEI(100, mu=10, sigma=2)
# library(gamlss)
# gamlss(dat~1, family=WEI)Run the code above in your browser using DataLab