nptol.int: Nonparametric Tolerance Intervals

Description

Provides 1-sided or 2-sided nonparametric (i.e., distribution-free) tolerance intervals for any continuous data set.

Usage

nptol.int(x, alpha = 0.05, P = 0.99, side = 1,
          method = c("WILKS", "WALD", "HM"), upper = NULL,
          lower = NULL)

Arguments

A vector of data which no distributional assumptions are made. The data is only assumed to come from a continuous distribution.

alpha

The level chosen such that 1-alpha is the confidence level.

The proportion of the population to be covered by this tolerance interval.

side

Whether a 1-sided or 2-sided tolerance interval is required (determined by side = 1 or side = 2, respectively).

method

The method for determining which indices of the ordered observations will be used for the tolerance intervals. "WILKS" is the Wilks method, which produces tolerance bounds symmetric about the observed center of the residuals by using

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:
alphaThe specified significance level.
PThe proportion of the population covered by this tolerance interval.
1-sided.lowerThe 1-sided lower tolerance bound. This is given only if side = 1.
1-sided.upperThe 1-sided upper tolerance bound. This is given only if side = 1.
2-sided.lowerThe 2-sided lower tolerance bound. This is given only if side = 2.
2-sided.upperThe 2-sided upper tolerance bound. This is given only if side = 2.

References

Bury, K. (1999), Statistical Distributions in Engineering, Cambridge University Press. Hahn, G. J. and Meeker, W. Q. (1991), Statistical Intervals: A Guide for Practitioners, Wiley-Interscience. Wald, A. (1943), An Extension of Wilks' Method for Setting Tolerance Limits, The Annals of Mathematical Statistics, 14, 45--55. Wilks, S. S. (1941), Determination of Sample Sizes for Setting Tolerance Limits, The Annals of Mathematical Statistics, 12, 91--96.

Examples

Run this code

## 90\%/95\% 2-sided nonparametric tolerance intervals for a 
## sample of size 20. 

set.seed(100)
x <- rlogis(20, 5, 1)
out <- nptol.int(x = x, alpha = 0.10, P = 0.95, side = 1,
                 method = "WILKS", upper = NULL, lower = NULL)
out

plottol(out, x, plot.type = "both", side = "two", x.lab = "X")