for m normal we have, from (A3),
P(R∣T) = Φ(Y2) - Φ(Y1), (A8b)
where Φ is the unit normal distribution function.
2. Relative discrepancy. Let Wi = 1 + (-1)iB, i = 1, 2. The relative rule (A2b) is then. (A7)
Assuming, the upper inequality is satisfied when . (A8)
The random variable z has mean and variance,,
Hence defining, i = 1,2 (A9a)
analogously to the Absolute Discrepancy case, we have
P(R∣T) = Φ(Z2) - Φ(Z1). (A9b)
Now we require expressions for the standard deviations σT, σS, which depend on the source in the information processing chain.
Let τ be exponentially distributed with mean 1/λ. If λ = Λ is constant, then the number of counts, nT, accumulated in a fixed time has the Poisson distribution with
E(nT) E NT = Var(nT). (A10)
But since mT = KnT, and if K* = 1, we have immediately
σT = K[NT]1/2 = K[Λ(T -T0)]1/2. T 〉 T0. (A11)