# npbetolint: Nonparametric Beta-Expectation Tolerance Intervals In tolerance: Statistical Tolerance Intervals and Regions

## Description

Provides 1-sided or 2-sided nonparametric (i.e., distribution-free) beta-expectation tolerance intervals for any continuous data set. These are equivalent to nonparametric prediction intervals based on order statistics.

## Usage

 `1` ```npbetol.int(x, Beta = 0.95, side = 1, upper = NULL, lower = NULL) ```

## Arguments

 `x` A vector of data which no distributional assumptions are made. The data is only assumed to come from a continuous distribution. `Beta` The confidence level. `side` Whether a 1-sided or 2-sided tolerance interval is required (determined by `side = 1` or `side = 2`, respectively). `upper` The upper bound of the data. When `NULL`, then the maximum of `x` is used. `lower` The lower bound of the data. When `NULL`, then the minimum of `x` is used.

## Value

`nptol.int` returns a data frame with items:

 `Beta` The specified confidence level. `1-sided.lower` The 1-sided lower tolerance bound. This is given only if `side = 1`. `1-sided.upper` The 1-sided upper tolerance bound. This is given only if `side = 1`. `2-sided.lower` The 2-sided lower tolerance bound. This is given only if `side = 2`. `2-sided.upper` The 2-sided upper tolerance bound. This is given only if `side = 2`.

## References

Beran, R. and Hall, P (1993), Interpolated Nonparametric Prediction Intervals and Confidence Intervals, Journal of the Royal Statistical Society, Series B, 55, 643–652.

## See Also

`distfree.est`, `npregtol.int`, `nptol.int`

## Examples

 ```1 2 3 4 5 6 7 8 9``` ``` ## Nonparametric 90%-expectation tolerance intervals ## for a sample of size 100. set.seed(100) x <- rexp(100, 5) out <- npbetol.int(x = x, Beta = 0.90, side = 2, upper = NULL, lower = NULL) out ```

tolerance documentation built on Feb. 6, 2020, 5:08 p.m.