ci_quantile {confintr} R Documentation

## 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.

### 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).

### 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.

### 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.

ci_quantile.
x <- 1:100