Computational Statistics

TESTS FOR SHIFT ALTERNATIVES 117

We also can use simulation to determine bands. In contrast to the one-sample case we do not

have a given distribution from which to simulate. Under the hypothesis that the distributions

F and G do not differ for independent observations the joined vector (X

1

, . . . , X

n

, Y

1

, . . . , Y

m

)

is the vector of n + m independent random numbers with identical distribution F = G. Given

a data set, this relation can be used for simulation. Using a permutation π of the indices from

the vector Z = (X

1

, . . . , X

n

, Y

1

, . . . , Y

m

) a new vector Z

0

with Z

0

i

= Z

π(i)

is generated. The

first n components are used as simulated values (X

0

i