135
Table 5.1 Summary of the Test Statistics Considered in the
Monte Carlo for Scale.*
Test
Statistic
1
2
3
4
5
6
7
8
9
Description
CD statistic using Var^(CD)
CD statistic using Var2(CD)
CD statistic using Var^CCD)
nl n<
TM
ni >n,
r Tn1+ Tnc (i ,e >L1 L2 1)
(i.e. L j = 2 L,2 = 1 )
' Tni+ 2Tnc Ci.e.,Li-l,L2-2)
(i.e. ,Lj = l L 2 = 1)
(i.e..Lj-2,L2=1)
= T_ (M) + 2Tn (i.e.,L1-l,L2-2)
T = 2 T + T
Di j ^ n 1 n
nl n,
TM_ = T (M) + T
nlnc nl nc
TM = 2T (M) + T
n 1 nc nl nc
n i
Section
in Thesis
2.4
2.4
2.4
3.2
3.2
3.2
3 3
3.3
3.3
Tn,(M) denotes the T statistic of Section 3.3 which
1 n j
uses an estimate for the common location parameter.
random variables (denoted IK i = 1,2 . ,2n) were first
generated and then the following transformations were
applied:
Xli = ^U2i-1 1 ^ ^ 1_V ^ 1 ) 2 cos ( 2ttU2 )
X2i = (u2i-l1/(1_V) 1)/2 sin(2TrU2i)
where the parameter v (for bivariate pairs, v > 1) specifies
a particular Pearson Type VII distribution. To generate
bivariate pairs with scale parameters and o2 and
correlation p, the following transformation was applied: