confintr (version 0.1.0)

ci_quantile: Confidence Interval for a Population Quantile

Description

This function calculates confidence intervals for a population quantile. By default, distribution-free confidence intervals based on the binomial distribution are formed, see Hahn and Meeker. Alternatively, bootstrap confidence intervals are available.

Usage

ci_quantile(
  x,
  q = 0.5,
  probs = c(0.025, 0.975),
  type = c("binomial", "bootstrap"),
  boot_type = c("bca", "perc", "norm", "basic"),
  R = 9999,
  seed = NULL,
  ...
)

Arguments

x

A numeric vector.

q

A single probability value determining the quantile. Set to 0.5 for the median (the default).

probs

Error probabilites. The default c(0.025, 0.975) gives a symmetric 95% confidence interval.

type

Type of confidence interval. One of "binomial" (default), or "bootstrap".

boot_type

Type of bootstrap confidence interval ("bca", "perc", "norm", "basic"). Only used for type = "bootstrap".

R

The number of bootstrap resamples. Only used for type = "bootstrap".

seed

An integer random seed. Only used for type = "bootstrap".

...

Further arguments passed to boot::boot.

Value

A list with class cint containing these components:

• parameter: The parameter in question.

• interval: The confidence interval for the parameter.

• estimate: The estimate for the parameter.

• probs: A vector of error probabilities.

• type: The type of the interval.

• info: An additional description text for the interval.

Details

Bootstrap confidence intervals are calculated by the package "boot", see references. The default bootstrap type is "bca" (bias-corrected accelerated) as it enjoys the property of being second order accurate as well as transformation respecting (see Efron, p. 188).

References

1. Hahn, G. and Meeker, W (1991). Statistical Intervals. Wiley 1991.

2. Efron, B. and Tibshirani R. J. (1994). An Introduction to the Bootstrap. Chapman & Hall/CRC.

3. Canty, A and Ripley B. (2019). boot: Bootstrap R (S-Plus) Functions.

See Also

ci_quantile.

Examples

# NOT RUN {
x <- 1:100
ci_quantile(x)
ci_quantile(x, q = 0.25)
ci_quantile(x, q = 0.25, type = "bootstrap", R = 999)
# }