fweibull: ML estimation of classical Weibull distribution

In Renext: Renewal Method for Extreme Values Extrapolation

ML estimation of classical Weibull distribution

Description

Fast Maximum Likelihood estimation of the classical two parameters Weibull distribution.

Usage

fweibull(x, info.observed = TRUE, scaleData = TRUE, cov = TRUE,
         check.loglik = FALSE)

Arguments

x	Sample vector to be fitted. Should contain only positive non-NA values.
info.observed	Should the observed information matrix be used or the expected one be used?
scaleData	Should the data be scaled before estimation? If TRUE, the observations in x (which are positive) are divided by their mean value. The results are in theory not affected by this transformation, but scaling the data could improve the estimation in some cases.
cov	Should the covariance of estimates be computed?
check.loglik	If TRUE, the log-likelihood is recomputed using dweibull function with log = TRUE. The result is returned as a list element.

Details

The ML estimates are obtained thanks to a reparameterisation with \eta = scale^{1/shape} in place of shape. This allows the maximisation of a one-dimensional likelihood L since the \eta parameter can be concentrated out of L. This also allows the determination of the expected information matrix for [shape,\,\eta] rather than the usual observed information.

Value

A list

estimate	Parameter ML estimates.
sd	The (asymptotic) standard deviation for estimate.
cov	The (asymptotic) covariance matrix computed from theoretical or observed Information matrix.
eta	The estimated value for eta.

Note

The default value of info.observed was set to TRUE from version 3.0-1 because standard deviations obtained with this choice are usually better.

Author(s)

Yves Deville

See Also

weibplot for Weibull plots.

Examples

n <- 1000
set.seed(1234)
shape <- 2 * runif(1)
x <- 100 * rweibull(n, shape = 0.8, scale = 1)
res <- fweibull(x)

## compare with MASS
if (require(MASS)) {
   res2 <- fitdistr(x , "weibull")
   est <- cbind(res$estimate, res2$estimate)
   colnames(est) <- c("Renext", "MASS")
   loglik <- c(res$loglik, res2$loglik)
   est <- rbind(est, loglik)
   est
}

## Weibull plot
weibplot(x,
         shape = c(res$estimate["shape"], res2$estimate["shape"]),
         scale = c(res$estimate["scale"], res2$estimate["scale"]),
         labels = c("Renext 'fweibull'", "MASS 'fitdistr'"),
         mono = TRUE)

Renext documentation built on Aug. 30, 2023, 1:06 a.m.