Coverage for Nonparametric Tolerance Interval for Continuous Distribution
Compute the coverage associated with a nonparametric tolerance interval for a continuous distribution given the sample size, confidence level, coverage type (β-content versus β-expectation), and ranks of the order statistics used for the interval.
tolIntNparCoverage(n, conf.level = 0.95, cov.type = "content",
ltl.rank = ifelse(ti.type == "upper", 0, 1),
n.plus.one.minus.utl.rank = ifelse(ti.type == "lower", 0, 1),
ti.type = "two.sided")n |
vector of positive integers specifying the sample sizes.
Missing ( |
conf.level |
numeric vector of values between 0 and 1 indicating the confidence level of the tolerance interval. |
cov.type |
character string specifying the coverage type for the tolerance interval.
The possible values are |
ltl.rank |
vector of positive integers indicating the rank of the order statistic to use for the lower bound
of the tolerance interval. If |
n.plus.one.minus.utl.rank |
vector of positive integers related to the rank of the order statistic to use for
the upper bound of the tolerance interval. A value of
|
ti.type |
character string indicating what kind of tolerance interval to compute.
The possible values are |
If the arguments n, conf.level, ltl.rank, and
n.plus.one.minus.utl.rank are not all the same length, they are replicated to be the
same length as the length of the longest argument.
The help file for tolIntNpar explains how nonparametric β-content
tolerance intervals are constructed and how the coverage
associated with the tolerance interval is computed based on specified values
for the sample size, the confidence level, and the ranks of the order statistics used for
the bounds of the tolerance interval.
vector of values between 0 and 1 indicating the coverage associated with the specified nonparametric tolerance interval.
See the help file for tolIntNpar.
In the course of designing a sampling program, an environmental scientist may wish to determine
the relationship between sample size, coverage, and confidence level if one of the objectives of
the sampling program is to produce tolerance intervals. The functions
tolIntNparN, tolIntNparConfLevel, tolIntNparCoverage, and
plotTolIntNparDesign can be used to investigate these relationships for
constructing nonparametric tolerance intervals.
Steven P. Millard (EnvStats@ProbStatInfo.com)
See the help file for tolIntNpar.
# Look at how the coverage of a nonparametric tolerance interval increases with # increasing sample size: seq(10, 60, by=10) #[1] 10 20 30 40 50 60 round(tolIntNparCoverage(n = seq(10, 60, by = 10)), 2) #[1] 0.61 0.78 0.85 0.89 0.91 0.92 #--------- # Look at how the coverage of a nonparametric tolerance interval decreases with # increasing confidence level: seq(0.5, 0.9, by=0.1) #[1] 0.5 0.6 0.7 0.8 0.9 round(tolIntNparCoverage(n = 10, conf.level = seq(0.5, 0.9, by = 0.1)), 2) #[1] 0.84 0.81 0.77 0.73 0.66 #---------- # Look at how the coverage of a nonparametric tolerance interval decreases with # the rank of the lower tolerance limit: round(tolIntNparCoverage(n = 60, ltl.rank = 1:5), 2) #[1] 0.92 0.90 0.88 0.85 0.83 #========== # Example 17-4 on page 17-21 of USEPA (2009) uses copper concentrations (ppb) from 3 # background wells to set an upper limit for 2 compliance wells. The maximum value from # the 3 wells is set to the 95% confidence upper tolerance limit, and we need to # determine the coverage of this tolerance interval. tolIntNparCoverage(n = 24, conf.level = 0.95, ti.type = "upper") #[1] 0.8826538
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