Download PDF by : Advances in Computers, Vol. 21

ISBN-10: 0120121212

ISBN-13: 9780120121212

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Extra resources for Advances in Computers, Vol. 21

Example text

Since H4 provides little information concerning f(xil H,), the density f ( x i l H 4 ) should provide as little help as possible for testing against f(xilK4);f ( x i l H 4 ) should therefore be as close tof(xilK4) as possible. 3-5) f(XiIH4) = 2 (f' + f - ) The density f ( x i l H 4 ) has zero median, and hence belongs to H,; and f(x,lH,) closely resembles f ( x i l K 4 ) since f ( x i l H 4 ) has the same shape as If(x,IK4) on the positive and negative axes. 3-6) The ratio of the signal present density to the signal absent density in Eq.

3-5) f(XiIH4) = 2 (f' + f - ) The density f ( x i l H 4 ) has zero median, and hence belongs to H,; and f(x,lH,) closely resembles f ( x i l K 4 ) since f ( x i l H 4 ) has the same shape as If(x,IK4) on the positive and negative axes. 3-6) The ratio of the signal present density to the signal absent density in Eq. 3-8) If n, = Z~,,u(x,)is used to denote the number of positive observations, the likelihood ratio may be written using Eqs. 3-9) L ( x ) = (2p)"' [2(1 - p)]"-"+ Eq. 3-12) H4 Since it can be shown that the detector in Eq.

Unbiasedness is a simple and reasonable condition to impose on a detector. 6 Composite Hypotheses 29 F E K is never less than the level of the test. The reasonableness of requiring a test to be unbiased can be seen by noting that if the conditions given in Eq. 6-10) are not satisfied, the probability of accepting H will be greater under some distributions contained in the alternative K than in some cases when the hypothesis H is true. 6-11) Although Eq. 6-10) states the concept of unbiasedness quite clearly, it is difficult to employ this definition to find most powerful unbiased tests because of the presence of the inequalities.

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Advances in Computers, Vol. 21


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