A common assumption for whether an animal becomes sick when exposed to a chemical at dosage level x is to assume a threshold model, which supposes that each animal has a random threshold and will become ill if the dosage level exceeds that threshold. The exponential distribution has sometimes been used as the threshold distribution. For instance, a model considered in Freedman and Zeisel (“From Mouse to Man: The Quantitative Assessment of Cancer Risks,” Statistical Science, 1988, 3, 1, 3–56)

supposes that a mouse exposed to x units of DDT (measured in ppm) will contract cancer of the liver with probability

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p(x)=1-ex, x>0