Advanced Management Accounting Problems by Kenneth P. Gee

By Kenneth P. Gee

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795 P 1 B a Having obtained two stochastic matrices representing the transition probabilities for the January-March period, the que stion which then arises is one of how to combine their information in deriving an estimate of the stochastic matrix for March-April. This may be done in a variety of ways, but the approach which has been specifically advocated is one involving exponential weighting. Combining matrices by exponential weighting To explain this approach, it is necessary to define two new terms as follows.

447. 8 84, and so on . But since state 0 is a transient state , a pound in th at state can only be paid or pass from state 0 to state 1. 116 In general, the transition probabilities for movements from one state to another for k = 3 .. 5. 5. It is next necessary to compute the transition probabilities from state 4 (that is, from k = 7) . This is trickier , because of the existence of three , rather than two, possibilities. They are as follows: 1. There may be a transition from state 4 to pa yment, with a transition probability of t7p .

Combining matrices by exponential weighting To explain this approach, it is necessary to define two new terms as follows. Let: a represent the smoothing constant to be applied to the stochastic matrices . 6) From this approach , it would appear that obtaining the MarchApril average matrix A] must involve updating A z by reference to T]. 838 0 : ! 0917 ! 7926 From its third row downwards, the P column of A3 represents the transition probabilities for a pound from each of states G-4 to payment. If the transition probabilities are pre multiplied by the vector 1] showing the partial balance age structure of debts at the end of March, then a vector £4 is obtained showing the estimated aging of debtor balances including payments and bad debts.

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