KiRSTiNE Smith 
63 
Let the factor in curled brackets in (77) be for a skew distribution ^ {x) 
and Fq for the corresponding symmetrical distribution. 
We then have 
^ 0 = 7 ¥\ • 
The condition for a maximum or minimum other than that at a; = 0 is 
2>lii — |Lt4 > 0, 
or ^2 < 3, 
and as the denominator is positive we have in that case the maximum at x = 0. 
It is thus clear that the maxima of Fq between — 1 and 1 must be either at « = 0 
or at « = it 1 . 
We shall show that 
and that either [-^s],i-=i or [-f's],i.= -i > [-^o].r=±i- 
According to what has been proved in Section I (4) the coefficient of in (77) is 
positive, the denominator of (77) is therefore positive and we have 
L-^ s ~ oJ .i-=o — , r~r^ ■> > *J. 
We shall next compare F^ and F„ for x = i 1. 
N 
D 
N-S 
Putting [F,],^, 
we have [i^.]..=i = ^ 
where S = /x,^ - 2^1^, + lA ± 2 (1 - fx,^ - (^^ - ^^)] 
and e = ^3 _ 2^ija2ju.3 + /xj/i^ . 
g 
For - we find 
e 
Looking first at the case — ^ 0, we have 
and if we choose the value for which the other term of the numerator is < 0 
?<i. 
e 
When < 0 we see, from considering the form 
^ = 1 _ ^'1 (1 - f^i) - 2/^1^3 (1 - A^ a) ± 2 {fM, (1 - /xa) - (/x^ - ^,)} 
that for either a;=lora; = — 1 
?<i. 
e 
