Environmental Health Criteria 214

HUMAN EXPOSURE ASSESSMENT
Continuous probability distributions are described by their
probability density function (PDF), which provides the probability of
an outcome taking values in a small interval, and by their cumulative
distribution function (CDF), which describes the probability of an
outcome being less than a particular value. The PDF and CDF are
directly analogous to the concepts of a histogram and cumulative
probability distribution discussed in Section 4.2.
Probability models are used to make statements such as, "The
probability that the daily maximum ozone concentration will be greater
than 120 ng/litre today is 0.08." Such estimates can be based upon
empirical evidence (i.e., by looking at the number of observed
concentrations greater than 120 ng/litre in comparison with the total
number of observed concentrations) or by choosing a distribution and
parameters that describe the observed data. An example of the latter
would be to model the distribution of blood lead levels in Maltese
subjects as normally distributed with a mean of 243 µg/litre and
standard deviation of 70.9 µg/litre and to use the properties of the
distribution to estimate the probability. The amount of confidence in
the accuracy of the estimates is related to the amount of data
available and the sampling scheme used to collect the data, as well as
the degree to which the mathematical distribution fits the observed
data.
Two standard distributions commonly used in exposure assessment
for modelling continuous outcomes are the normal and the
lognormal distributions. The binomial and Poisson distributions
are often used in exposure studies as well. Many other probability
distributions are available which have more flexibility (Johnson &
Kotz, 1970a,b), but these four are frequently used and thus warrant
attention here.
4.3.1 Normal distribution
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6/1/2007