Derivation of the Estimates and Variances 

 It is necessary to define the following quantities : 



General 



Nj^ ■ Estimate of the number of hours of fishing effort on lakeshore 

 during period of D days . 



Nf ■ Estimate of the number of individual fishermen on lakeshore 

 during period of D days . 



Nc " Estimates of the total catch on lakeshore during period of 

 D days. 



^ (Nh) ■ Estimate of variance of N^ due to internal variation in the 

 complete census only. 



s (Nq) ■ Estimate of variance of Ng due to internal variation in the 

 complete census only. 



D •* Number of days in the period under consideration. (In the case 

 of the Yellowstone Lake and River censuses, D = lU«) 



T " Length of time unit in which the data are classified. T = 

 1 hour in this study. 



Complete Census 



Hj^ " Number of hours of effort counted during the i'''^ hour. 



Hr ■ Number of hours fished by the r'th man during the entire fishing 

 day, 



H » S H^ « 2 H " Total number of hours of effort recorded during 

 i -'■ r ~ 



during the complete census. 

 Cr " Total (day's) catch for the r'*'^ man. 

 i " Index of hour. i=l, 2, ..., I. 

 I ■ Total number of hours during a fishing day. 

 r ■ Index of fisherman, r = 1, 2, ..., R. 

 E <« Total number of individual fishermen in the complete census. 



3li 



