Sometimes it's the parameters that define the distribution that you need to find. Suppose, for example, you have conducted a Students-t test for equal means and the result is borderline. Maybe your two samples differ from each other, or maybe they don't; based on the result of the test you can't be sure. A legitimate question to ask then is "How many more measurements would I have to take before I would get an X% probability that the difference is real?" Parameter finders can answer questions like this, and are necessarily different for each distribution. They are implemented as static member functions of the distributions, for example:
students_t::find_degrees_of_freedom( 1.3, // difference from true mean to detect 0.05, // maximum risk of falsely rejecting the null-hypothesis. 0.1, // maximum risk of falsely failing to reject the null-hypothesis. 0.13); // sample standard deviation
Returns the number of degrees of freedom required to obtain a 95% probability that the observed differences in means is not down to chance alone. In the case that a borderline Students-t test result was previously obtained, this can be used to estimate how large the sample size would have to become before the observed difference was considered significant. It assumes, of course, that the sample mean and standard deviation are invariant with sample size.