# NOT RUN {
# Generate 20 observations from a binomial distribution with
# parameters size=1 and prob=0.2, then estimate the 'prob' parameter.
# (Note: the call to set.seed simply allows you to reproduce this
# example. Also, the only parameter estimated is 'prob'; 'size' is
# specified in the call to ebinom. The parameter 'size' is printed
# inorder to show all of the parameters associated with the
# distribution.)
set.seed(251)
dat <- rbinom(20, size = 1, prob = 0.2)
ebinom(dat)
#Results of Distribution Parameter Estimation
#--------------------------------------------
#
#Assumed Distribution: Binomial
#
#Estimated Parameter(s): size = 20.0
# prob = 0.1
#
#Estimation Method: mle/mme/mvue for 'prob'
#
#Data: dat
#
#Sample Size: 20
#----------------------------------------------------------------
# Generate one observation from a binomial distribution with
# parameters size=20 and prob=0.2, then estimate the "prob"
# parameter and compute a confidence interval:
set.seed(763)
dat <- rbinom(1, size=20, prob=0.2)
ebinom(dat, size = 20, ci = TRUE)
#Results of Distribution Parameter Estimation
#--------------------------------------------
#
#Assumed Distribution: Binomial
#
#Estimated Parameter(s): size = 20.00
# prob = 0.35
#
#Estimation Method: mle/mme/mvue for 'prob'
#
#Data: dat
#
#Sample Size: 20
#
#Confidence Interval for: prob
#
#Confidence Interval Method: Score normal approximation
# (With continuity correction)
#
#Confidence Interval Type: two-sided
#
#Confidence Level: 95%
#
#Confidence Interval: LCL = 0.1630867
# UCL = 0.5905104
#----------------------------------------------------------------
# Using the data from the last example, compare confidence
# intervals based on the various methods
ebinom(dat, size = 20, ci = TRUE,
ci.method = "score", correct = TRUE)$interval$limits
# LCL UCL
#0.1630867 0.5905104
ebinom(dat, size = 20, ci = TRUE,
ci.method = "score", correct = FALSE)$interval$limits
# LCL UCL
#0.1811918 0.5671457
ebinom(dat, size = 20, ci = TRUE,
ci.method = "exact")$interval$limits
# LCL UCL
#0.1539092 0.5921885
ebinom(dat, size = 20, ci = TRUE,
ci.method = "adjusted Wald")$interval$limits
# LCL UCL
#0.1799264 0.5684112
ebinom(dat, size = 20, ci = TRUE,
ci.method = "Wald", correct = TRUE)$interval$limits
# LCL UCL
#0.1159627 0.5840373
ebinom(dat, size = 20, ci = TRUE,
ci.method = "Wald", correct = FALSE)$interval$limits
# LCL UCL
#0.1409627 0.5590373
#----------------------------------------------------------------
# Use the cadmium data on page 8-6 of USEPA (1989b) to compute
# two-sided 95% confidence intervals for the probability of
# detection at background and compliance wells. The data are
# stored in EPA.89b.cadmium.df.
EPA.89b.cadmium.df
# Cadmium.orig Cadmium Censored Well.type
#1 0.1 0.100 FALSE Background
#2 0.12 0.120 FALSE Background
#3 BDL 0.000 TRUE Background
#...
#86 BDL 0.000 TRUE Compliance
#87 BDL 0.000 TRUE Compliance
#88 BDL 0.000 TRUE Compliance
attach(EPA.89b.cadmium.df)
# Probability of detection at Background well:
#--------------------------------------------
ebinom(!Censored[Well.type=="Background"], ci=TRUE)
#Results of Distribution Parameter Estimation
#--------------------------------------------
#
#Assumed Distribution: Binomial
#
#Estimated Parameter(s): size = 24.0000000
# prob = 0.3333333
#
#Estimation Method: mle/mme/mvue for 'prob'
#
#Data: !Censored[Well.type == "Background"]
#
#Sample Size: 24
#
#Confidence Interval for: prob
#
#Confidence Interval Method: Score normal approximation
# (With continuity correction)
#
#Confidence Interval Type: two-sided
#
#Confidence Level: 95%
#
#Confidence Interval: LCL = 0.1642654
# UCL = 0.5530745
# Probability of detection at Compliance well:
#--------------------------------------------
ebinom(!Censored[Well.type=="Compliance"], ci=TRUE)
#Results of Distribution Parameter Estimation
#--------------------------------------------
#
#Assumed Distribution: Binomial
#
#Estimated Parameter(s): size = 64.000
# prob = 0.375
#
#Estimation Method: mle/mme/mvue for 'prob'
#
#Data: !Censored[Well.type == "Compliance"]
#
#Sample Size: 64
#
#Confidence Interval for: prob
#
#Confidence Interval Method: Score normal approximation
# (With continuity correction)
#
#Confidence Interval Type: two-sided
#
#Confidence Level: 95%
#
#Confidence Interval: LCL = 0.2597567
# UCL = 0.5053034
#----------------------------------------------------------------
# Clean up
rm(dat)
detach("EPA.89b.cadmium.df")
# }
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