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Confidence Interval for Any Quantile

Source: R/quantileCI.R
quantileCI.Rd

Calculates the confidence interval for any quantile. Although bootstrapping might be a good approach for getting senisble confidence intervals there's sometimes need to have a nonparameteric alternative. This function offers one.

Usage

quantileCI(
  x,
  conf.level = 0.95,
  sides = c("two.sided", "left", "right"),
  method = c("exact", "boot"),
  probs = seq(0, 1, 0.25),
  na.rm = FALSE,
  ...
)

Arguments

x

a (non-empty) numeric vector of data values.

conf.level

confidence level of the interval.

sides

a character string specifying the side of the confidence interval, must be one of "two.sided" (default), "left" or "right" (abbreviations allowed).
"left" would be analogue to a "greater" hypothesis in a t.test.

method

defining the type of interval that should be calculated (one out of "exact", "boot"). Default is "exact". See Details.

probs

numeric vector of probabilities with values in [0,1]. Values up to 2e-14 outside that range are accepted and moved to the nearby endpoint.

na.rm

logical. Should missing values be removed? Defaults to FALSE.

...

bootstrap arguments can be provided by the dots argument. See boot::boot.ci() for details.

Value

A numeric matrix with one row per element of probs and columns:

est

estimated quantile.

lci

lower confidence interval bound.

uci

upper confidence interval bound.

For the "exact" method, the attribute conf.level reports the achieved coverage (which may differ from the requested level).

Details

The "exact" method corresponds to the way the confidence interval for the median is calculated in SAS.
The boot confidence interval type is calculated by means of boot::boot.ci() with default type "basic".

See also

DescToolsX::quantileX, quantile(),

Other ci.location: meanCI(), meanCIn(), meanDiffCI(), medianCI(), sumCI()

Examples


x <- mtcars$mpg
quantileCI(x, probs=0.25, na.rm=TRUE)
#>        est  lci  uci
#> 25% 15.425 13.3 17.8
#> attr(,"conf.level")
#> [1] 0.9555407

quantileCI(x, na.rm=TRUE)
#>         est  lci  uci
#> 0%   10.400   NA 10.4
#> 25%  15.425 13.3 17.8
#> 50%  19.200 15.8 21.4
#> 75%  22.800 21.0 30.4
#> 100% 33.900 30.4   NA
#> attr(,"conf.level")
#> [1] 1.0000000 0.9555407 0.9649180 0.9555407 1.0000000
quantileCI(x, conf.level=0.99, na.rm=TRUE)
#>         est  lci  uci
#> 0%   10.400   NA 10.4
#> 25%  15.425 13.3 19.2
#> 50%  19.200 15.5 22.8
#> 75%  22.800 19.2 30.4
#> 100% 33.900 30.4   NA
#> attr(,"conf.level")
#> [1] 1.0000000 0.9912891 0.9929996 0.9912891 1.0000000

# multiple probs
quantileCI(1:100, method="exact" , probs = c(0.25, 0.75, .80, 0.95))
#>       est lci uci
#> 25% 25.75  17  34
#> 75% 75.25  67  84
#> 80% 80.20  73  89
#> 95% 95.05  90  99
#> attr(,"conf.level")
#> [1] 0.9512948 0.9512948 0.9532735 0.9514464
quantileCI(1:100, method="boot" , probs = c(0.25, 0.75, .80, 0.95))
#>       est      lci   uci
#> 25% 25.75 16.38201 33.75
#> 75% 75.25 66.18216 83.25
#> 80% 80.20 72.20000 87.20
#> 95% 95.05 90.00000 98.05