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
and scale
parameter
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} )](images/proeq28.gif)
Thus, in this case, the intercept parameter,
b0, and the regression parameter,
b1, are related to
and
by
![b_1 & = & \frac{1}{\sigma} \
b_0 & = & -\frac{\mu}{\sigma} \](images/proeq29.gif)
Note: The parameter
is not equal to the
standard deviation of the population of tolerances
for the logistic and extreme value distributions.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.