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In a population of accounts each unit has a book value, y, (known) and a true but unknown value, x. For a random sample of accounts the true values are observed. Using the posterior from a stepwise Bayes model this simulates possible values of D, the sum of the differences between the the book values and the true values. The 0.95 quantile of this posterior will yield an approximate 95 upper confidence bound for T for most populations and will be less conservative than the Stringer bound.
simulateD(ysmp,xsmp,yunsmp ,n,pgt,pwa,R)numeric vector of book values for the units in the sample
the corresponding true values for the units in the sample
numeric vector of the book values for the units not in the sample
an integer which is the size of the sample
numeric vector of prior guesses for the taints
weights corresponding to the taints that appear in the posterior
an integer which is the number of simulated values of D returned
A vector of lenght R containing simulated values of D
For a given unit (y-x)/x is its taint. pgt is a prior guess for the possible taints in the population. pwt specifies how much weight the prior guess pgt should have in the posterior. When all the taints are assumed to be nonnegative then the Stringer bound is often used. Setting both pqt and pwt equal to one yields a slightly shorter bound than that of Stringer's.
Meeden, G. and Sargent, D. (2007) Some Bayesian methods for two auditing problems. Communications in Statistics --- Theory and Methods, 36, 2727--2740. 10.1080/03610920701386802.
# NOT RUN {
y <- rgamma(500,5)
x <- y
dum <- sample(1:500,50)
x[dum] <- x[dum]*runif(50,.05,0.5)
smp <- sample(1:500,40)
quantile(simulateD(y[smp],x[smp],y[-smp],40,1,1,1000),0.95)
# }
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