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