Page 122 - Introduction to Statistical Pattern Recognition

1 04 Introduction to Statistical Pattern Recognition

(3.159)

On the other hand, when (3.152) is used to compute p,

1
p =- (3.160)
R
2

}
This is based on E (x I ai } = (Bi+l)/ai and Var{ x I mi = (Pi+l)/aF as in (2.56)
and (2.57).
In many applications, PI and P2 are equal or close to each other. There-
fore, in order to simplify the discussion of comparing (3.159) and (3.160). let
us assume PI = P2 = P. Then,

(3.161)

and

r 7
(3.162)

Figure 3-19 shows the relation between and pLR for various values of p. For
a given p and po, (3.161) is solved to find the corresponding aI/az, which is
inserted to (3.162) to compute p,. The values for are selected between 0
and 2 which corresponds to E" between 0.5 and 0.068 from Fig. 3-17. Figure
3-19 indicates that pg could be significantly different from p0, particularly for
smaller P's.

Variable transformation: The power transformation of (3.77) tends to
convert a gamma distribution to a normal-like one. Therefore, it must make pg