nptl function

Nonparametric Upper Tolerance Limit

Given a random sample of size n from a continuous distribution, then, with a confidence level of at least $\gamma$, at least 100p percent of the population will be below the kth largest value in the sample.

nptl(n , p = 0.95, gam = 0.95)

Arguments

• n: the sample size
• p: probability for Xp the 100pth percentile. Default is 0.95
• gam: one-sided confidence level $\gamma$. Default is 0.95

Returns

• k: index of the order statistic

References

Sommerville, P. N. (1958), "Tables for Obtaining Non-Parametric Confidence Limits," Annals of Mathematical Statistics, 29, 599-601.

Author(s)

E. L. Frome

Note

The maximum non-detect must be less than the kth largest value.

Examples

data(beTWA)
k<- nptl(length(beTWA[,1]))
rev(sort(beTWA[,1]))[k]