Page 105 - Introduction to Statistical Pattern Recognition

3 Hypothesis Testing 87

PI
t=ln--, (3.102)
p2
(3.103)
a* = a: = a: = 27 ,
Thus, when the density function of the likelihood ratio is normal, the probabili-
ties of error can be obtained from the table of @(.).

General Error Expression

Error expression: Before computing the error of the quadratic classifier
for normal distributions, let us express the error of a classifier in a general
form. Let a classifier be

(3.104)

Then, the ol -error is

(3.105)

where u(.) is the step function. The second line is obtained by using the fact
that the Fourier transform of a step function, u(h), is [K&(O) + lijw]. Like-
wise, the 02-error is

(3.106)

Then, the total error becomes