I’m trying to identify the 95% confidence interval of either the mean or the median of non-normal data generated through Monte Carlo simulations using R. I’ve already applied both the bootstrapping method as well as the Wilcoxon signed rank test as suggested on the following thread: How do I calculate confidence intervals for a non-normal distribution?. However the resulting CIs from both tests seem suspiciously small, especially given the overall spread of the data .
#Install truncdist - to truncate distributions install.packages("truncdist") library(truncdist) #Monte Carlo simulations S1 <- rtrunc(10000, spec = "lnorm",a=0, b=1600, meanlog=4.4166,sdlog=1.1334) S2 <- rtrunc(10000, spec = "logis",a=0, location = 97.056, scale = 50.86) S3 <- rtrunc(10000, spec = "norm", a=0, mean=11.3,sd=4.45) #Calculate averages of Monte Carlo simulations SampleS <- matrix(c(S1,S2,S3),nrow = 10000,ncol = 3) finalSmeans <- rowMeans(SampleB) hist(finalS) #Install package to run bootstrap install.packages("resample") library(resample) #Bootstrap CI for mean bootmean <- bootstrap(finalS, mean, R=1000) CI.bca(bootmean) 2.5% 97.5% mean 91.99672 94.8231 #Bootstrap CI for median bootmedian <- bootstrap(finalS, median, R=1000) CI.bca(bootmedian) 2.5% 97.5% median 74.54763 76.87361 #Wilcoxon test for median CIs wilcox.test(finalS, conf.int = TRUE, conf.level = 0.95) Wilcoxon signed rank test with continuity correction data: finalS V = 50005000, p-value < 2.2e-16 alternative hypothesis: true location is not equal to 0 95 percent confidence interval: 80.58888 82.58312 sample estimates: (pseudo)median 81.5794
Have I done something wrong? Are these tests appropriate to use when evaluating distributions generated through Monte Carlo simulations? Or are there more robust tests out there that I'm not aware of?