Tolerance Distribution

The PROBIT Procedure

Tolerance Distribution

For a single independent variable, such as a dosage level, the models for the probabilities can be justified on the basis of a population with mean $\mu$ and scale parameter $\sigma$ of tolerances for the subjects. Then, given a dose x, the probability, P, of observing a response in a particular subject is the probability that the subject's tolerance is less than the dose or

$P = F ( \frac{x - \mu}{\sigma} )$

Thus, in this case, the intercept parameter, b₀, and the regression parameter, b₁, are related to $\mu$ and $\sigma$ by

$b_1 & = & \frac{1}{\sigma} \ b_0 & = & -\frac{\mu}{\sigma} \$

Note: The parameter $\sigma$ is not equal to the standard deviation of the population of tolerances for the logistic and extreme value distributions.

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