Animal Cognition: Proceedings of the Harry Frank Guggenheim Conference, June 2-4, 1982

By H. S. Terrace; H. L. Roitblat et al. | Go to book overview

, (A4)

and

. (A5)

Defining

, (A6a)

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,

,

and

.

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.


B. PACEMAKER: POISSON

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)

-485-

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