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

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
sd(asymptotic) standard deviation for estimate
cov(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

library(MASS) 
n <- 1000
shape <- 2*runif(1)
x <- 100*rweibull(n, shape = 0.8, scale = 1)
res <- fweibull(x)
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
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)