the input data are correct is the demonstration that the model does, in
fact, yield estimates of Toa which are quite close to the best estimate
available.

The evidence, Figures 1 through 9, in support of the lognormal hypothesis

is fairly persuasive but it may not meet the requirements for rigorous
mathematical proof.
The best data available for testing the lognormal
hypothesis are the plutonium concentrations in vegetation and soil
samples from Area 13, Tables 1 and 2.
Sampling within strata was random,
but the maximum number of samples from a given stratum is 47, too few to
provide an accurate measure of the true frequency distribution.
Strata 1
and 2 were sampled only in part, i.e., no samples were collected in the
parts of these strata located outside the fenced portion of Area 13.
In
other words, the sampling design is adequate and efficient for inventory

purposes but leaves much to be desired if one's statistical objective is

to determine the shape of a frequency distribution curve.
A better
approach for this purpose would be to collect between 100 and 200 nonstratified random samples from strata 3, 4, 5, and 6 which are completely

enclosed by the inner fence.

In spite of these "faults" in the sampling

design, the histograms do show that the logarithms of the sample values
in Tables 1 and 2 are symmetrically distributed around their means and
that the actual distributions, whatever they may be, can be represented
as lognormal.

An alternative to the lognormal hypothesis is simply to use the arithmetic means of ls Co. I_, and C_
to generate synthetic samples of I u
The only_ objective to this procedure is that the coefficients of varia-

tion (s/x) are so large, for some inputs, that normal variation would be

expected to include a predictable percentage of negative values which,
of course, have no meaning with respect to the factors of Equation 1.

To determine whether the occurrence of negative values in synthetic

samples affects the overall results of the simulation model and, at the
same time, whether or not the usefulness of the simulation model depends
on the assumption of lognormal distributions, it was decided to repeat
the simulation study using arithmetic means and standard deviations
instead of the means and standard deviations of logarithms.
New estimates of x + s were calculated for I.

and I_.

The procedure for

generating the synthetic samples upon which the new estimates were based

was the same as used to obtain the estimates listed in Tables 5 and 7,
except that the total sample size was increased from n = 500 to n =
1,000.
The synthetic means and standard deviations thus obtained were

I 6,526 + 2,396 g/day and I_

= 227.3 + 669.5 g/day.

(N.B.

The mean

and standard deviations of In 8.5 g, in 57.3 g, and ln 278 g, i.e.,
3.93866 + 1.74636, were used to estimate the synthetic values given
above for I_
because the arithmetic mean and standard deviation of these
three samples, 115 + 144 g, would indicate an average soil ingestion

rate much lower than the 250 to 500 g/day suggested, as a "reasonable
estimate," by Smith (1977). With only three site-specific samples to go

on, it is difficult to defend any estimate of I_.
The estimate given
above is judged to be the best available at present.)

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