430 
PEOFESSOR K. PEARSON AND MISS A. LEE ON THE DISTRIBUTION 
deferred to its modal 
given by 
where 
and 2^ — 7^0 
(or maximum) ordinate this frequency distribution is 
y — d" .(ii.) 
7 = ^p-sZ/xg, a = 2g37g3, 
^ \/27r (^5 + 1) c I'jjP 
\/ 27ryU,2 r (+ 1) 
(ii!-) 
In order that this curve should fit a skew frequency distribution it is theoretically 
necessary that 
6 + 3^2 ~ 2^3 
should be zero, or at least that it should in statistical practice be small. 
The theory of this curve is discussed, ‘ Phil. Trans,,’ A, vol. 186, p. 373. It is 
shown in the same memoir that if 
6 + SySi - 2^3 > 0 
the generalised probability curve 
2 / = 2 /o (1 + xla^y'‘^ (1 — .(iv.) 
will be found suitable, whereas if 
6 + 3/82 — 2^3 < 0 
tlie generalised probability curve 
y = yQ 
1 
{1 + {xjaYY^ 
Q—v tan“i(.r/«) 
(v.) 
will, in a greed variety of cases, represent the frequency. Methods for determining 
the constants of these curves are fully described, and these methods have been 
adopted in the present paper. 
Of the curves (ii.), (iv,), and (v.), it may be noted that (ii.) has a range of frequency 
limited in one direction, (iv.) a range limited in both directions, while (v.), like the 
normal distribution (i.), has a range unlimited in both directions. 
When a frequency distribution can be satisfactorily described by a curve of form 
(ii.), then it is generally possible to obtain a skew binomial representing, with a fair 
degree of accuracy, this distribution,! 
In the ‘Phil. Trans.’ memoir above referred to, some Cambridge barometric data 
are dealt with, and it is shown for this case : 
(i.) lhat 6 ■+ 3^82 — 2,83 is > 0 , and this barometric frequency therefore fits a curve 
of limited range. 
* The mean ordinate is given by y-^ = (-fhlLiy L . 
\ p / e 
t The rule is not general, just as it is sometimes, but not always, possible to represent a noinial 
distribution by a symmetileal binomial. 
