The package is available from GitHub, R-universe or CRAN.
Once installed the package needs to be loaded:
A very simple example to compute two different 95% confidence
intervals for the 25th percentile based on a sample of size 25 from a
standard normal distribution. The true value is
qnorm(0.25)=-0.6744898.
x <- rnorm(25)
#Compute 25% quantile of the sample as inverse of ECDF (i.e. type=1)
quantile(x, prob=0.25, type=1)
#> 25%
#> -0.565907
#Compute confidence interval for it (two methods)
quantileCI::quantile_confint_exact(x=x, p=0.25, conf.level=0.95)
#> [1] -1.317529 -0.111795
quantileCI::quantile_confint_nyblom(x=x, p=0.25, conf.level=0.95)
#> [1] -1.1841388 -0.2038905In this example we look at the use of quantile as part of the water monitoring in the city of Fling. For details see the blog post Beware the Argument: The Flint Water Crisis and Quantiles.
# Load Flint data, see blog post for details
data(flint)
#Compute type=5 quantile as in https://www.youtube.com/watch?v=9pql00zr700
quantile(flint$lead, probs=0.9, type=5)
#> 18.8 [ppb]
##Compute type=1
quantile(flint$lead, probs=0.9, type=1)
#> 18 [ppb]
##Compute corresponding non-parametric 90% CI
quantileCI::quantile_confint_exact(flint$lead, p=0.9, conf.level=0.9)
#> Units: [ppb]
#> [1] 10 43The qci_coverage_one_sim function can be used to
investigate the coverage of the confidence interval method using
simulation. Below a small example showing that the exact method is too
conservative, i.e. the coverage is larger than the nominal level. This
means that the intervals wider than necessary.
# Investigate coverage of the exact CIs
quantile_confints <- function(x, p, conf.level, x_is_sorted=FALSE) {
if (!x_is_sorted) { x <- sort(x)}
data.frame(exact=quantile_confint_exact(x=x, p=p, conf.level=conf.level))
}
# Coverage is above the nominal 90%
set.seed(123)
sim <- unlist(replicate(1000,qci_coverage_one_sim(quantile_confints, n=nrow(flint), rfunc=rnorm, qfunc=qnorm, p=0.9, conf.level=0.9)))
mean(sim)
#> [1] 0.932