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Compute the confidence level associated with a nonparametric
tolIntNparConfLevel(n, coverage = 0.95,
ltl.rank = ifelse(ti.type == "upper", 0, 1),
n.plus.one.minus.utl.rank = ifelse(ti.type == "lower", 0, 1),
ti.type = "two.sided")
vector of positive integers specifying the sample sizes.
Missing (NA
), undefined (NaN
), and infinite (Inf
, -Inf
)
values are not allowed.
numeric vector of values between 0 and 1 indicating the desired coverage of the
vector of positive integers indicating the rank of the order statistic to use for the lower bound
of the tolerance interval. If ti.type="two-sided"
or
ti.type="lower"
,
the default value is ltl.rank=1
(implying the minimum value of x
is used
as the lower bound of the tolerance interval). If
ti.type="upper"
, this argument
is set equal to 0
.
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
n.plus.one.minus.utl.rank=1
(the default) means use the
first largest value, and in general a value of
n.plus.one.minus.utl.rank=
ti.type="lower"
, this argument is set equal to 0
.
character string indicating what kind of tolerance interval to compute.
The possible values are "two-sided"
(the default), "lower"
, and
"upper"
.
vector of values between 0 and 1 indicating the confidence level associated with the specified nonparametric tolerance interval.
If the arguments n
, coverage
, 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
See the help file for tolIntNpar
.
tolIntNpar
, tolIntNparN
, tolIntNparCoverage
,
plotTolIntNparDesign
.
# NOT RUN {
# Look at how the confidence level of a nonparametric tolerance interval increases with
# increasing sample size:
seq(10, 60, by=10)
#[1] 10 20 30 40 50 60
round(tolIntNparConfLevel(n = seq(10, 60, by = 10)), 2)
#[1] 0.09 0.26 0.45 0.60 0.72 0.81
#----------
# Look at how the confidence level of a nonparametric tolerance interval decreases with
# increasing coverage:
seq(0.5, 0.9, by = 0.1)
#[1] 0.5 0.6 0.7 0.8 0.9
round(tolIntNparConfLevel(n = 10, coverage = seq(0.5, 0.9, by = 0.1)), 2)
#[1] 0.99 0.95 0.85 0.62 0.26
#----------
# Look at how the confidence level of a nonparametric tolerance interval decreases with the
# rank of the lower tolerance limit:
round(tolIntNparConfLevel(n = 60, ltl.rank = 1:5), 2)
#[1] 0.81 0.58 0.35 0.18 0.08
#==========
# 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. There are 6 observations
# per well, and 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
# Here we will modify the example and determine the confidence level of the tolerance
# interval when we set the coverage to 95%.
tolIntNparConfLevel(n = 24, coverage = 0.95, ti.type = "upper")
# [1] 0.708011
# }
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