The test checks how well each output member corresponds to the valid range of possible values. For example, for an exponential distribution with parameters a and b all the output members xi should lie within the range a ≤ xi < ∞. A value xi < 1 is impossible, that is, the fact that the variate X of exponential distribution with parameters a and b acquires a value less than a is an impossible event (not to be confused with a null event). Any output member lying outside the valid range causes an error.
Such a test is necessary because statistical tests (for example, distribution moments test or chi-square test) cannot detect a small number (if compared with the total sample size) of xi values falling outside the valid range.
The test gives a certain quantity K of random numbers that lie outside the valid range of values. The test is considered passed, if K = 0, and failed otherwise.