KUNGL. SV. VET. AKADEMIENS HANDLINGAR. BAND 58- NIO 3- 9 



In the above form we shall apply the ^4-function in the following. 



The parameters m,, ra 2 , a,, <r 2) r, /% are called the characteristics of the correla- 

 tion function. 



To distinguish them from the parameters A {j , which are also called characterist- 

 ics, we shall call the fa the /3-characteristics of the correlation surface. 



(4) General ierminology. For the benefit of readers not familiar with correla- 

 tion work we shall here explain the notation generally used. It is mostly due to 

 Pearson. 



Any fixed value of x or y will be written x p and y q . 



Taking out all the individuals having the variate x within the limits x p ± 1 /no l 

 we shall generally find that the corresponding values of y form a statistical series 

 of variation. This series of y-values is called an x-array of y:s. 



Similarly f ixing a value of y between the limits y q ± l \i w 2 we obtain an ?/-ar- 

 ray of x:s. 



Each a-array of y:s, as well as each y-array of x:s, has a frequency curve 

 which we shall denote by F a (y) and F Vt (x) respectively. We then have 



F Xp (y) = F(x p ,y), 



F !/q (x) = F(x,y g ). 



The relative number of individuals in each of the x-arrays gives the total fre- 

 quency distribution of the x:s. We call it F x {x); the total frequency distribution 

 of the y:s we call F 2 (y) and it is given by the relative number of individuals in 

 the separate ?/-arrays. 



We thus have 



F^^jdyFix^) 



F 2 (y)= dxF(x,y) 



The mean of the y:s in an a;-array is called y Xp or shortly y x . The dispersion 

 we denote by o Xp {y): the skewness by Sx p (y); the excess by Ex p (y). The moments 

 about the mean y Xp in an x-array we denote by v„{y) Xp . 



We then have 



y Xp = I dyF(x p , y)y: F x (.r p ) , 



— 00 



CO 



"V.'/) = I dy F(x p , y) (y - y Xp Y : F t (x p ) , 



— CO 



K. Sv. Vet. Akad. Handl. Band 58. N:o 3. 



