# NOT RUN {
# Generate 20 observations from a lognormal distribution with parameters
# meanlog=0 and sdlog=1. Use tolIntLnorm to estimate
# the mean and standard deviation of the log of the true distribution, and
# construct a two-sided 90% beta-content tolerance interval with associated
# confidence level 95%.
# (Note: the call to set.seed simply allows you to reproduce this example.)
set.seed(250)
dat <- rlnorm(20)
tolIntLnorm(dat, coverage = 0.9)
#Results of Distribution Parameter Estimation
#--------------------------------------------
#
#Assumed Distribution: Lognormal
#
#Estimated Parameter(s): meanlog = -0.06941976
# sdlog = 0.59011300
#
#Estimation Method: mvue
#
#Data: dat
#
#Sample Size: 20
#
#Tolerance Interval Coverage: 90%
#
#Coverage Type: content
#
#Tolerance Interval Method: Exact
#
#Tolerance Interval Type: two-sided
#
#Confidence Level: 95%
#
#Tolerance Interval: LTL = 0.237457
# UTL = 3.665369
# The exact two-sided interval that contains 90% of this distribution
# is given by: [0.193, 5.18].
qlnorm(p = c(0.05, 0.95))
#[1] 0.1930408 5.1802516
# Clean up
rm(dat)
#==========
# Example 17-3 of USEPA (2009, p. 17-17) shows how to construct a
# beta-content upper tolerance limit with 95% coverage and 95%
# confidence using chrysene data and assuming a lognormal distribution.
# The data for this example are stored in EPA.09.Ex.17.3.chrysene.df,
# which contains chrysene concentration data (ppb) found in water
# samples obtained from two background wells (Wells 1 and 2) and
# three compliance wells (Wells 3, 4, and 5). The tolerance limit
# is based on the data from the background wells.
head(EPA.09.Ex.17.3.chrysene.df)
# Month Well Well.type Chrysene.ppb
#1 1 Well.1 Background 19.7
#2 2 Well.1 Background 39.2
#3 3 Well.1 Background 7.8
#4 4 Well.1 Background 12.8
#5 1 Well.2 Background 10.2
#6 2 Well.2 Background 7.2
longToWide(EPA.09.Ex.17.3.chrysene.df, "Chrysene.ppb", "Month", "Well")
# Well.1 Well.2 Well.3 Well.4 Well.5
#1 19.7 10.2 68.0 26.8 47.0
#2 39.2 7.2 48.9 17.7 30.5
#3 7.8 16.1 30.1 31.9 15.0
#4 12.8 5.7 38.1 22.2 23.4
with(EPA.09.Ex.17.3.chrysene.df,
tolIntLnorm(Chrysene.ppb[Well.type == "Background"],
ti.type = "upper", coverage = 0.95, conf.level = 0.95))
#Results of Distribution Parameter Estimation
#--------------------------------------------
#
#Assumed Distribution: Lognormal
#
#Estimated Parameter(s): meanlog = 2.5085773
# sdlog = 0.6279479
#
#Estimation Method: mvue
#
#Data: Chrysene.ppb[Well.type == "Background"]
#
#Sample Size: 8
#
#Tolerance Interval Coverage: 95%
#
#Coverage Type: content
#
#Tolerance Interval Method: Exact
#
#Tolerance Interval Type: upper
#
#Confidence Level: 95%
#
#Tolerance Interval: LTL = 0.0000
# UTL = 90.9247
#----------
# Repeat the above example, but estimate the mean and
# coefficient of variation on the original scale
#-----------------------------------------------
with(EPA.09.Ex.17.3.chrysene.df,
tolIntLnormAlt(Chrysene.ppb[Well.type == "Background"],
ti.type = "upper", coverage = 0.95, conf.level = 0.95))
#Results of Distribution Parameter Estimation
#--------------------------------------------
#
#Assumed Distribution: Lognormal
#
#Estimated Parameter(s): mean = 14.5547353
# cv = 0.6390825
#
#Estimation Method: mvue
#
#Data: Chrysene.ppb[Well.type == "Background"]
#
#Sample Size: 8
#
#Tolerance Interval Coverage: 95%
#
#Coverage Type: content
#
#Tolerance Interval Method: Exact
#
#Tolerance Interval Type: upper
#
#Confidence Level: 95%
#
#Tolerance Interval: LTL = 0.0000
# UTL = 90.9247
# }
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