Q2 Z2,(Q2) Z2(Q2) - Institute for Water Resources - U.S. Army

Notc that the first subscript of a.., j b. and ci refers to the
lj 1j
distribution subscript of the numerator, and the second subscript
to the subscript of the distribution in the denominator. If it
2 2 2
is possible to assume that a. = .0ij
equation (10) becomes,
i ij
= 0ij'
n.(X )
(13) in 1
h.(XJ
(14)
(15)
a . b!. X. . with
1] ij
2 2 2
a:. = - 0'229
1] / J.]
2
b' = (.0. - .U..)/0..
ij llj 3 13 / 1)
Now the criteria for R 1 given by (7) can be rewritten as
in
n (X ) ' q
1 21 2/
- A' 1 + b2 ' ln q
n (X )
12 X 21 > 1
2 21
n
1
(X
31
) 43,
in r-r71---7 ( = ai 3 bi 3 X31 > in 'qv if the variances are
3‘ 31!
equal. Similar sets of criteria can be derived for R 2 and R 3 . The
critical values X 21 and X 31 which define R 1 are those which make the
left -hand side of the inequalities (14) equal to their right-hand side.
Each of these critical values can also be used to define regions of
classification when the choice is restricted to two modes. It is then
easy to compute the chances of misclassifying an origin or firm with
characteristic X ij when the choice is restricted to modes i and J.
With i U. > U the probability of misclassifying an observation
lj j ij
from w as from w, is
7
Rij 2 .1 •1(Xii i./4 )2 /1.44 : dXij
(16) P(j/i) = (2 jo ie) A
_ft =AO