\\\ Table* for Statistician* tun/ Ilinun-trii-iaiix \ I 



Now on the assumption of a normal distribution : 



^'..r* * .-N- 



Jx V27TO- 



-No* I" ag 



J* 



Here Table IX (p. 22) shows that if s be odd, w,(oo ) = '398,9423, i.e. 

 :in.l (p. 23) if s be even, m, (oo ) = '500,0000. 



Hence in obtaining the moment coefficients of the tail, about the mean of the 

 whole population, m, (x') should be subtracted from '398,9423 or from '500,0000 

 before the results are multiplied by (a !)(* 3) ... 2 or (s l)(s 3) ... 1, when 

 s is odd or even respectively. It is convenient to term p, (oo ) /*(X) the com- 

 plementary incomplete moment function of order a*. 



For s=l and a = 2, we have 



ji/t,' = ffN {TO, (oo ) - TO, (*')}, 

 /<,' = <r*N {m, (oo ) - TO* (a;')}, 



for in this case the multiplying factors to proceed from m t (x') to p,(x') are both 

 unity. 



Now x 1 = xj<7 can be found when n is known from Tables II or III. Hence we 

 have for the distance of centroid of tail from its stump, and for the square of its 

 standard-deviation about its centroid : 



d = /*,' - h'o- = a- P^ {m, (oo ) - wi, (a; 1 )} - A'l 



Of course m, (ao ) n^x') is the z of Sheppard's Tables II and III. 

 Returning to our numerical example, we have from Table IX (p. 22) : 

 (45905) = '030,6721 + '5905 [162049] - 1 ('5905) ('4095) [26358] 



= -039,9222, 



TO, (oo ) - TO, (-45905) = '359,02. 



Found directly from Sheppard's Tables, it equals '35905. 

 Similarly from Table IX (p. 23) : 



m, ('45905) = -008,1136 + -5905 [73,162] - }(-5905) ('4095) [30661] 



= -012,0630, 

 and TO, (oo)-m, (-45905) = -487,9370. 



* It is the function used by Dr Alice Lee and myself, Biometrika, Vol. vi. p. 65 to form Table XI, 

 P. 2fi, but by an oversight not adequately distinguished in symbol from n, (x') of p. 60 of the same memoir. 



