quantileCI: Confidence Intervals for Quantiles

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/quantileCI.R

Description

These functions can be used to compute confidence intervals for quantiles (including median).

Usage

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quantileCI(x, prob = 0.5, conf.level = 0.95, method = "exact",
           minLength = FALSE, na.rm = FALSE)
medianCI(x, conf.level = 0.95, method = "exact",
         minLength = FALSE, na.rm = FALSE)
madCI(x, conf.level = 0.95, method = "exact", minLength = FALSE,
      na.rm = FALSE, constant = 1.4826)

Arguments

x

numeric data vector

prob

quantile

conf.level

confidence level

method

character string specifing which method to use; see details.

minLength

logical, see details

na.rm

logical, remove NA values.

constant

scale factor (see mad).

Details

The exact confidence interval (method = "exact") is computed using binomial probabilities; see Section 6.8.1 in Sachs and Hedderich (2009). If the result is not unique, i.e. there is more than one interval with coverage proability closest to conf.level, then a matrix of confidence intervals is returned. If minLength = TRUE, an exact confidence interval with minimum length is returned.

The asymptotic confidence interval (method = "asymptotic") is based on the normal approximation of the binomial distribution; see Section 6.8.1 in Sachs and Hedderich (2009).

Value

A list with components

estimate

the sample quantile.

CI

a confidence interval for the sample quantile.

Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

References

L. Sachs and J. Hedderich (2009). Angewandte Statistik. Springer.

See Also

binom.test, binconf

Examples

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## To get a non-trivial exact confidence interval for the median
## one needs at least 6 observations
set.seed(123)
x <- rnorm(8)
## exact confidence interval not unique
medianCI(x)
madCI(x)

## minimum length exact confidence interval
medianCI(x, minLength = TRUE)
madCI(x, minLength = TRUE)

## asymptotic confidence interval
medianCI(x, method = "asymptotic")
madCI(x, method = "asymptotic")

## confidence interval for quantiles
quantileCI(x, prob = 0.4)
quantileCI(x, prob = 0.6)

Example output

$call
medianCI(x = x)

$estimate
       50% 
0.09989806 

$CI
           [,1]     [,2]
[1,] -1.2650612 1.558708
[2,] -0.5604756 1.715065
attr(,"(exact) confidence level")
[1] 0.9609375

$call
madCI(x = x)

$estimate
      50% 
0.7571578 

$CI
           [,1]     [,2]
[1,] 0.04357313 2.162832
[2,] 0.04357313 2.394646
attr(,"(exact) confidence level")
[1] 0.9609375

$call
medianCI(x = x, minLength = TRUE)

$estimate
       50% 
0.09989806 

$CI
[1] -0.5604756  1.7150650
attr(,"(exact) confidence level")
[1] 0.9609375

$call
madCI(x = x, minLength = TRUE)

$estimate
      50% 
0.7571578 

$CI
[1] 0.04357313 2.16283208
attr(,"(exact) confidence level")
[1] 0.9609375

$call
medianCI(x = x, method = "asymptotic")

$estimate
       50% 
0.09989806 

$CI
[1] -1.265061  1.558708
attr(,"(asymptotic) confidence level")
[1] 0.95

$call
madCI(x = x, method = "asymptotic")

$estimate
      50% 
0.7571578 

$CI
[1] 0.04357313 2.16283208
attr(,"(asymptotic) confidence level")
[1] 0.95

$call
quantileCI(x = x, prob = 0.4)

$estimate
       40% 
0.01037122 

$CI
[1] -1.265061  1.558708
attr(,"(exact) confidence level")
[1] 0.9746842

$call
quantileCI(x = x, prob = 0.6)

$estimate
      60% 
0.1956134 

$CI
[1] -0.5604756  1.7150650
attr(,"(exact) confidence level")
[1] 0.9746842

MKmisc documentation built on Aug. 8, 2021, 5:06 p.m.