npbetol.int {tolerance}

Nonparametric Beta-Expectation Tolerance Intervals

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

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

 
## 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