Fit a missing parameter value

Usually we first specify a probability distribution (its name and all its parameter values) and then PyQRS calculates probabilities associated with a given \(x\)-value or the \(x\)-value (quantile), given a probability.

In PyQRS 3 and 4 it is also possible to find an unknown parameter value, given the distribution name, given the remaining parameter value(s), given the \(x\)-value and given the cumulative probability. The method is a heuristic, not necessarily leading to a solution and if a solution is found, it may not be the only possible solution. But it will work in most cases.

The procedure is as follows:

  1. Specify the distribution (name),
  2. Specify all known parameters by entering their value(s), each time finishing with hitting 'Enter'. Then only one parameter value will be left open. This unknown parameter should be real-valued, not integer-valued.
One parameter (p) left open
Specify x-value
  1. Specify the \(x\)-value and the cumulative probability. The latter value is specified not only if you enter it under the 'cdf'-tab, but also if you enter it in the red edit field under the 'pdf'/'pmf'-tab if the distribution is continuous. You may even specify the cumulative probability by entering its complement in the blue edit field under the 'pdf'/'pmf'-tab.
  2. After you specified the last value by hitting 'Enter', PyQRS will try to fit the missing parameter value and show it under the 'Specification'-tab.
Specify cumulative probability
The missing parameter value is computed