ccxviii Tables for Statisticians and Biometridans [XLV XLVf 



If we write as = a sin 0, the probability integral of this curve or 



rx i r+a 



\(l+a x ) = ydx ydx 



J a I J -a 



r 



~ 2 + 2 7771 W' 



cos* m + l 0d0 



Jo 



Hence a x = f cos 2 "' +1 0d0 IT* cos Zm+1 0d0. 



Jo / Jo 



Putting m = \n, we shall write 



Jo /Jo 



whence the probability integral can be found by the addition of ^. 



Type VII Pearson curve takes the form 



" =y Flf 



and is a symmetrical curve corresponding to J3\ = and /3 2 > 3. 



Write x = a tan 0, and the probability integral of this curve becomes 



(iv). 



Writing 2m 3 = n, this is 



| 4- I g (n + 1 ) (ii bis). 



Lastly considering the Type I symmetrical C7-curve, 



L. 



i-- 



a 2 



we note that for finite frequency m* must lie between and + 1, and that these 

 values correspond to the limits of /r? 2 = l'S and TO. Throughout /8 1 = 0. 



The probability integral is obtained by writing x = a sin 0, as in the first case, 



and 



re 



I 



COS c/ Ctu 



Jo 

 > = M9-5!3 2 )/(3-&). 



