XLV1II] liiirntlnctbm cc-.\\\ 



in the c.-usos of <M*<), fa(x) and <jn(x). W.- thus MC that tli.- present 

 Table will give the juvu of any portion of i-iiln-r of tin; liv.ju,-ii-y curves 



I 



if 7/t be even as low as 7. 



TABLES XLVII XLVIII. 



.For ascertaining the values of Incomplete B-functions for high value* of t/ie 

 Powers. (J. Wishart, Biowetrika, Vol. xix. pp. 138.) 



The Incomplete B-function from to x is : 



B* (p> </> = r xp ~ i <! 



Jo 

 The Complete B-function is : 



ri 

 B(p,q)=\ 



Jo 



and their ratio is expressed by 



The value of the Incomplete B-function can always be obtained from a knowledge 

 of I x (p, q) by using Tables of the Complete F-function. 



The object of the present tables is to supplement the Tables of the Incomplete 

 B-function, which will be published shortly. Those tables extend from values of 

 p, q = 0, to values = 50, 50. They thus exclude cases in which p and q are 

 either or both greater than 50. Such cases require special consideration, which 

 has been provided by H. E. Soper* and by J. Wishart in the paper referred to 

 above. 



We shall write our Incomplete B-function ratio in the form 





so that we are finding the probability integral of the curve of Type I 



y = y Q x l (l-x) m ................................. (iii), 



where the range is treated as the unit of abscissal measurement. 

 We place here one or two well-known results for this curve : 



Mean = 5 = (J + !)/(/ + * + 2) ............................. (iv), 



.......................................... (v), 



Standard Deviation = <r = V(J + l)(w + 1)/ {(I + m + 2f(l + m + 3)} ...(vi). 



* Tractt for Computers, No. vii. Cambridge University Press. 

 an. ff 



