49
Case 1 = ^2 known,
Ho: ai = a2 an<^ Ka: o< a 2
That is, the marginal distributions have the same known
f
location parameter but, under Hfl, X2^ has a larger scale
I
parameter than X^ A possible contour of an absolutely
continuous distribution of this form was given in Figure 2.
Case 2 p j = pi 2 unknown,
a 1 = a 2 and Ha
a L < a 2
Here, the marginal distributions have the same unknown
location parameter but, under Ha, X2 ^ has a larger scale
parameter than X^
(Note, for both cases, the alternative has been stated in
the form for a one sided test. The procedure which will be
presented can easily be adapted for the other one-sided or a
two sided alternative. The latter is discussed at the end
of this chapter )
In Sections 3.2 and 3.3, tests statistics for Case 1
and Case 2, respectively, will be presented which are
nonparametrically distribution-free conditional on N ^ = n ^
and Nc = n9+n^. In both cases, the test statistics can be
viewed as a linear combination of two independent test
statistics T and T where T is a statistic based only
nl nc nl
on the n^ uncensored observations, while Tn will be a
statistic based on the n£ = n2 + n3 type 2 and 3 censored
observations. The conditioning of the random variables