occur at a point that is devoid ol data. In either 

 event, the moments always give the "balance 

 point'' of the distribution, and we therefore 

 consider the moments to be valid indicators ol 

 the distribution of events in space, especially 

 when the moments are considered in the con- 

 text of the distribution from which the moments 

 are computed. 



We wish to emphasize also that the spatial 

 statistics discussed in this paper should not be 

 construed as estimates of the parameters of a 

 bivariate normal distribution, but rather as 

 indices of spatial central tendency, dispersion, 

 and orientation. To emphasize our point we 

 compare some typical examples of spatial 

 statistics for effort andCPUE with correspond- 



ing marginal normal distributions that have the 

 same parameter values as the spatial statis- 

 tics. These typical examples show the mar- 

 ginal distribution of effort and CPUE for Janu- 

 ary 1957 (fig. 7). From these we can see that 

 the first moment is a reasonable indicator of a 

 modal value for CPUE and longitudinal effort, 

 but that the latitudinal moment for effort lies 

 between the equatorial and North Pacific fishing 

 grounds. The latitudinal distribution of CPUE 

 tends to be more concentrated than if it corre- 

 sponded to a normal distribution. The longitu- 

 dinal CPUE and effort tend to be less concen- 

 trated than a corresponding normal distribution. 

 The latitudinal distribution of effort is, how- 

 ever, a special case, since it clearly represents 



-04 

 3 

 02 



a I 







08 

 07 

 06 

 5 

 04 

 3 

 02 

 Ol 

 - 



o 

 o 

 o 



L^mf 



140° 160° 180° 



LONGITUDINAL POSITION 



20° 30° 40° 



LATITUDINAL POSITION 



140° 160° 180° 



LONGITUDINAL POSITION 



20° 30° 40° 



LATITUDINAL POSITION 



Figure 7. --Relation between spatial statistics (January 

 1957) and normal probability distribution for effort and 

 CPUE (in numbers of fish per hundred hooks). 



