fweibull: ML estimation of classical Weibull distribution

Description

Fast Maximum Likelihood estimation of the classical two parameters Weibull distribution

Usage

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

Arguments

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?

check.loglik

If TRUE, the log-likelihood is recomputed using dweibull function with log = TRUE. The result is returned as a list element.

Value

A list
estimateParameter ML estimates.
sdThe (asymptotic) standard deviation for estimate.
covThe (asymptotic) covariance matrix computed from theoretical or observed Information matrix.
etaThe estimated value for eta.

Details

The ML estimates are obtained thanks to a reparametrisation 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.

Examples

Run this code

n <- 1000
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)