Managerial Monitoring of a Single Data Stream

Cover Managerial Monitoring of a Single Data Stream
Managerial Monitoring of a Single Data Stream
Michael Edmond Francis Treacy
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Then p(sQ|d) is a step function of d.
1 d d^ For values of r between zero and one, p(s^!d) has values between the two extremes. This is diagrammed in Figure 2.
18 Figure 2 The difference d^ may now be interpreted as the difference for which the manager would not change his prior judgement: p(s Id ) = p'(s ). For P'(s ) = p'(s ) = 1/2, we would expect that d^ = 0. If the distribution of d is symmetric about d, then d is also the expected difference prior to the receipt of y. Later in this paper
..., we shall develop an explicit formulation for d in terms of other primitives.
For intermediate r values, p(s |d) as a function of d is probably not linear, but it may be approximated by a linear function, through the point [d, p'(s )], as shown in Figure 3.
19 ?(s. \i'i Figure 3 The slope of the intermediate section of the linear approximation depends upon r and a scale factor. A simple function for this slope, m', is: A r m' = -m A > (21) d^ 1-r A/d» is simply a scale factor.


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