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:
- Specify the distribution (name),
- 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.
- 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.
- 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.