# ci_kurtosis: Confidence Interval for the Kurtosis In confintr: Confidence Intervals

## Description

This function calculates bootstrap confidence intervals for the population kurtosis, see Details. Note that we use the version of the kurtosis that equals 3 for a theoretical normal distribution.

## Usage

 ```1 2 3 4 5 6 7 8 9``` ```ci_kurtosis( x, probs = c(0.025, 0.975), type = "bootstrap", boot_type = c("bca", "perc", "norm", "basic"), R = 9999, seed = NULL, ... ) ```

## Arguments

 `x` A numeric vector. `probs` Error probabilites. The default c(0.025, 0.975) gives a symmetric 95% confidence interval. `type` Type of confidence interval. Currently not used as the only type is "bootstrap". `boot_type` Type of bootstrap confidence interval c("bca", "perc", "norm", "basic"). `R` The number of bootstrap resamples. `seed` An integer random seed. `...` 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. Efron, B. and Tibshirani R. J. (1994). An Introduction to the Bootstrap. Chapman & Hall/CRC.

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

`moments`, `ci_skewness`.

## Examples

 ```1 2 3``` ```set.seed(1) x <- rnorm(100) ci_kurtosis(x, R = 999) ```

### Example output

```	Two-sided 95% bootstrap confidence interval for the population
kurtosis based on 999 bootstrap replications and the bca method

Sample estimate: 3.007653
Confidence interval:
2.5%    97.5%
2.455576 3.776262
```

confintr documentation built on July 2, 2020, 1:51 a.m.