FOUNDATIONS OF THEORETICAL STATISTICS. 
341 
Example :—Determine the intrinsic accuracy of an error curve of Type IV. and the 
efficiency of the method of moments in location and scaling. 
Since 
~Ti ?'+ 1 v + 2 v + 4 
0 =- ==5 -;— > 
v + 4 +1" 
a 
r + 4 +i 
n r+lr+2r+4 
and the intrinsic accuracy of the curve is 
a 
1 Y T 1 x T 2 v + 4 
"~2 
— 2 
hut 
r + 4 +U 
a~ 
Y 2 + v 2 
n y 2 y- 1 
therefore the efficiency of the method of moments in location is 
Y Y 
-1 (r + 4 2 + d J ) 
When 
y +1 y + 2 r + 4 (y 2 + v 2 ) 
0 . Ave have for curves of Type VII. an efficiency of location 
6 
(3) 
r+lr+2 
The efficiency of location of these curves vanishes at r — 1, at which value the standard 
deviation becomes infinite. Although values down to —1 give admissible frequency 
curves, the conventional limit at which curves are reckoned as heterotypic is at r — 7. 
For this value the efficiency is 
49 121 +y 3 
132 ' 49 + 1' 2 ’ 
which varies from 91*67 per cent, for the symmetrical Type VII. curve, to 37*12 per 
cent, when v -> oo and the curve to Type V. 
Turning to the question of scaling, we find 
whence 
and 
jy-i = _ >-+lR>;+4 + ,») 
Y + 4“ +V 2 
2 r +1 
7’+4 ’ 
2 _ a? ?* + 4 _ 
n ’2 r+1' 
3 B 
VOL. CCXXII.-A. 
