The test checks how well each output member corresponds to the valid range of possible values. For example, for an exponential distribution with parameters
ball the output members xi should lie within the range
a ≤ x
< ∞. A value
i< 1 is impossible, that is, the fact that the variate
Xof exponential distribution with parameters
bacquires a value less than
ais 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
ivalues falling outside the valid range.
Interpreting Final Results
The test gives a certain quantity
Kof random numbers that lie outside the valid range of values. The test is considered passed, if
K= 0, and failed otherwise.