0
$\begingroup$

Is there a way to find out which percentiles are being bounded by the interval? Say I calculate a 2-sided tolerance interval for 95% of the population with 95% confidence interval. How do I find out whether this interval is using 0-95%, 1-96%, 2-97%, and so on percentiles?

The end game is that I want to calculate a (sort of) margin of error on a non-parametric tolerance interval, by calculating the difference between the upper tolerance interval and the percentile it's bounding.

EDIT: am I missing the point entirely? Is the 2-sided interval always centered around the median? So in the case of the 95%, is it always estimating the 2.5th and 97.5th percentiles?

Thank you!

data (only a subset of my original data; does not fit any parametric distribution well, whether transformed or not).

df <- structure(list(Val = c(7.8, 11.5, 9, 9.3, 9.2, 8.4, 8.6, 8.6, 
9.3, 8.6, 8.6, 6.6, 7.9, 5.6, 7.9, 8.4, 8.7, 9.5, 9.3, 8.8, 7.7, 
8.8, 8.8, 9.6, 7.9, 9.1, 10.3, 9, 8.1, 6.6, 10.4, 7.6, 9.1, 8.2, 
8.4, 8.1, 9.1, 15.4, 7.8, 8.1, 11.2, 8.5, 6.6, 9.3, 9.7, 7.6, 
5.7, 8.5, 8.9, 10, 8.3, 9.1, 8.2, 7, 8.2, 8.5, 6.8, 8.7, 6.4, 
8.3, 7.8, 7, 8.2, 5.6, 8.6, 8.9, 8.5, 7.6, 10.5, 12.3, 13.3, 
11.1, 11, 6.6, 7.1, 7, 8.2, 6.9, 10, 11, 9, 11, 10, 17, 13, 16, 
9, 8, 13, 9, 11, 11, 8, 13, 10, 11, 11, 14, 10, 11)), .Names = "Val", row.names = c(480L, 
484L, 632L, 634L, 653L, 654L, 656L, 658L, 659L, 660L, 663L, 671L, 
674L, 676L, 681L, 684L, 685L, 690L, 691L, 692L, 693L, 695L, 697L, 
699L, 700L, 704L, 705L, 706L, 708L, 710L, 713L, 715L, 722L, 723L, 
724L, 725L, 726L, 728L, 731L, 732L, 746L, 747L, 748L, 751L, 752L, 
754L, 756L, 757L, 758L, 759L, 760L, 762L, 763L, 766L, 770L, 774L, 
776L, 780L, 783L, 785L, 786L, 788L, 789L, 790L, 793L, 794L, 796L, 
798L, 819L, 824L, 878L, 910L, 926L, 1066L, 1079L, 1083L, 1084L, 
1085L, 1479L, 1480L, 1544L, 1545L, 1546L, 1580L, 1601L, 1610L, 
1611L, 1612L, 1615L, 1616L, 1617L, 1619L, 1651L, 1653L, 1658L, 
1662L, 1663L, 1668L, 1672L, 1673L), class = "data.frame")

library(tolerance)
interval <- normtol.int(x = df$Val, alpha = 0.05, P = 0.95, side = 2, 
    method = "HE", log.norm = FALSE)

subset of possible quantiles (0-5 in top row, 95-100 in bottom row, just for illustration)

matrix(quantile(df$Val, probs = c(seq(0, 0.05, 0.01), seq(0.95, 1, 0.01))), 
    nrow = 2, byrow = T)
$\endgroup$

1 Answer 1

0
$\begingroup$

The tolerance intervals ARE centered around the median, so the question is moot.

$\endgroup$
1
  • $\begingroup$ They are centered around the mean. $\endgroup$ Jul 24, 2017 at 17:47

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.