374 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28

It is really remarkable that the II curves, which relate to
he mixed model, stay very near to the I curves of the exponential
 model, even though the weight attributed to the expoaential
 element is but 2/3. This is due to the fact that the
coefficient A in the mixed model has a value very near that
which it takes in the exponential model, so that the 3(8) functions
 of model I and II have approximately the same three first
moments (1).

General Comments

540. It is certainly very surprising at first sight to find that
for small values of w and for large values of n, the model
considered has very different properties from those of the
exponential and para-exponential models, though for w=o it
is identical to the exponential model and for w=1 identical to
the para-exponential model.
For the first and second, for example,

4

B ~ i.

for

1-0=4%

whereas for w=o0.10 and # sufficiently great, À has a value
very near 5, and ®_ can even become greater than any value ().
It may first be noted that no illusions should be had about
small values of w, since large values of n can have a greater
influence, with correspondingly greater deviation of the model
irom the exponential.

A 4 336.
(?) $ 532 and 535.

‘'11] Allais - pag. 278