Renext (version 3.1-4)

fweibull: 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)

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.

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.

Author

Yves Deville

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.

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)