950 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 



These may be written as 



n -\- A 



and 



y= ^. 



7 



The first of these shows the estimated calling rate as a pooled combination 

 of the conditional estimate A/T, considered in the last section, and an 

 estimate n/h based on the initial state. This latter estimate has the form 



calls in progress 



mean holding time ' 



and so is intuitively reasonable, since b/h = a. The second equation 

 exhibits our estimate of 7 as a pooled combination of the conditional | 

 estimate H/Z and the ratio a/n. This ratio is acceptable as an estimate ; 

 of 7, since a/b = 7 and b = E{n\ is the average value of n. 



If we substitute, in the right-hand sides of these eciuations, the condi- 

 tional estimators A/T, H/Z, and Z/H for a, 7, and h, respectively, we 

 obtain simple, intuitive estimators which include the influence of the 

 initial state ?i, and show how it decreases with increasing T. Thus 



n + A 

 H^ 



^^ H 



estimates a, 



estimates 7. 



VIII OTHER ESTIMATORS 



Additional estimators may be arrived at by intuitive considerations, 

 or by modifying certain maximum likelihood estimators. Some estimators 

 so obtained are important because they use more of the information 

 available in an observation than do the conditional estimators dc and 

 7c , without being so complicated iunctionally that we cannot easily 

 study their statistical properties. 



