Environmental Health Criteria 214

HUMAN EXPOSURE ASSESSMENT
binary responses. The possible responses can be generally labelled as
success or failure. Often we are not interested in a single outcome,
but rather in the number of successes (k) and failures (n - k) for
a specific number (n) of repeated independent trials for the
outcome. The probability of exactly k successes in n independent
trials, given a probability of success (p) in a single trial, is
given by the binomial probability distribution ( P k ) in Table 10.
For example, assume daily exceedances of an ozone air quality
standard are independent events in a study of 1-year and 3-year time
periods. Let k be a random variable describing the total number of
exceedances encountered in a 1-year period ( n = 365 days). Further
assume from historical data that the expected number of exceedance
days each year is 1, thus p = 1/365 = 0.00274. The calculated
probabilities of k days of exceedance per year are shown in Table
12. Examination of the resulting probabilities in this example reveals
a right-skewed distribution with the greatest probability occurring
between k = 0 and k = 4 days.
4.3.4 Poisson distribution
Some exposure-related measurements are expressed as a rate of
discrete events, i.e., the number of times an event occurs per unit
time, such as the frequency (times per week) that a person consumes an
ocean fish containing a methylmercury concentration greater than
5.0 ppm. The Poisson distribution is used for describing potentially
unlimited counts or events that take place during a fixed period of
time (i.e., a rate), where the individual events are independent of
one and other. The Greek letter lambda is typically used to denote the
average or expected number of counts per unit time. In a Poisson
distribution, the parameter lambda also describes the variance of the
random variable. We can think about this intuitively by noting that as
the expected number of counts or events increases (i.e., the rate of
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