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 x

i

should lie within the range

a ≤ x

i

< ∞

. A value

x

i

< 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

x

i

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.