For all continuous distributions handled by inverse cumulative probability, the inverse of the cumulative distribution function (inverse CDF) exists and is unique if 0 < p < 1.
Here are cases when the ICDF may not exist:
- For all real numbers (for example, normal), inverse CDF is not defined for either p = 0 or p = 1.
- For all numbers greater than some value (for example, gamma), inverse CDF is defined for p = 0 but not for p = 1.
- Only on an interval (for example, beta), inverse CDF is defined for p = 0 and p = 1.
Whenever inverse CDF is not defined, Minitab returns a missing value (*) for the result.
For discrete distributions, the situation is more complicated. Suppose you compute the CDF for a binomial with n = 5 and p = 0.4. In this case, there is no value x such that the CDF is 0.5. For x = 1, the CDF is 0.3370; for x = 2, the CDF jumps up to 0.6826.
If the inverse cumulative probabilities are displayed in a table and not stored in a column, both values of x are displayed. If the inverse cumulative probabilities are stored, the larger of the two values is stored in the worksheet column.