KUNGL. SV. VET. AKADEMIENS HANDLINGAR. BAND 58- NIO 3. 



, (X — m) 2 



Defining the moments by 



»>i= I ttx{x — mYF(x), 



the coefficients are expressed by ' 



m = the arithmetic mean of the variate. 







(T* = »/, , 







[3 -4, = -»3, 







|£4, = v 4 — 3*;, 







[5.4,,— - /-, + 10j' 3 >' 2> 







|6^ G = r 6 + 30 v* — 15 *v',- 





The quantities 



3-^3 Q 



and 





34« 



are called by Charlier the skewness (Pearson's skewness with negative sign) and 

 the excess in the variation of x. 



(3) Special case for two variates. Taking now the case of two variates the 

 correlation function will be [x and y being reckoned from any origin) 



4 ' • ' />£■' ox 2 dy dxdy- oy s 



4 ''' '/'■'•..'/) , , ^rp(x,y) d* (p(x,y) . O^pjx.y) 0* <f>(x,y ) 



+ " i0 Ox* + 3l fo; 3 0« 0*W f ,3 r/.r<V U4 tfw 3 + 



+ A » df ■ + - etC - 



Here we have to put 



, 1^ [ (as — roi) 2 _ g (* — mi) (y — roa) (y — »na) 3 I 



Defining the moments by 



1 See Charlier. Loe. cit. Ser. II u:r 4. It should be observed that there is a printer's error in the 



formula for A . 



