Credible interval for median of Weibull distribution
Alternative proposed by Varin Sacha using the package weibulltools with delta method (a little bit modified to present only the median and the CI): library(weibulltools) x <- rweibull(100000, 2, 2) data <- reliability_data(x = x, status = 1) ml <- ml_estimation(x = data, distribution = "weibull") conf <- confint_fisher(x = ml, b_lives = 0.5, direction = "x") The results are: > as.numeric(conf[conf$prob == 0.5, c(4, 1, 5)]) [1] 1.657227 1.663275 1.669346 The true median was : > 2*log(2)^(1/2) [1] 1.665109 Let try if the average estimate by Fisher method for 1,000 samples is biased or not: library(weibulltools) library(pbmcapply) k <- pbmclapply(1:1000, FUN=function(i) { x <- rweibull(100000, 2, 2) data <- reliability_data(x = x, status = 1) ml <- ml_estimation(x = data, distribution = "weibull") conf <- confint_fisher(x = ml, b_lives = 0.5, direction = "x") return(as.numeric(conf[conf$prob == 0.5, 1])) }, mc.c