normal distributions. Ellett and Brownell (1964) suggest the gamma
distribution may be preferred to the lognormal distribution. Eberhardt

and Gilbert (1975) made an extensive study of how to distinguish these
two distributions and concluded that this is difficult for less than 200
observations.
Extensive Monte Carlo simulations were done to reach this

conclusion.

Forsythe et al.

(1975) compared the fit of the gamma and

lognormal distributions for the concentration of DDT in earthworms and
concluded that both fit the data equally well.
Figure 1 shows the
similarity of the lognormal and gamma probability density functions for
a variety of coefficients of variation and expected value equal 1.
Given that both these distributions appear to explain contaminant data
equally well, I want to explore the implication of selecting one of
these two distributions in estimating the expected value of concentration.

Some investigators (Eberhardt and Gilbert, 1973) have suggested using

the median of the observed data to measure central tendency when a
portion of the samples are below detection limits.
I believe that the
median may be quite useful for answering some questions, but that usually
the expected value is the desired measure.
This paper presents the

results of Monte Carlo simulations studies of estimating the expected

value (EX) for these two distributions.

Link and Koch (1975) explored the bias which may result when the lognormal estimator of expected value is used for distributions other than

lognormal. They found that a large negative bias (up to 97%) may result
when the distribution of the logarithmically transformed variable is

heavier tailed than the normal distribution.
However, no bias was found
when the logarithmically transformed variable has less tail area than
the normal distribution.
They did not consider lognormal estimation
with gamma distributed data.

ESTIMATORS

First the estimation of EX for the lognormal distribution will be considered.
The density function is given by Aitchison and Brown (1976):

f(x) = ——1_exp

co x vin
¥y

- +an x - Wd”

20°

¥

(x > 0;5 06 Oy > 0, -»< My < )

610

dx

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