Under the RP-PPS method, the system of prorating IS the
same but the probabilities
(4.13) (2.3~) (3)
The estimator Y., Eq. (3.2), can be written In a form
to the idea of prorating path fruit to terminal
Let Pi::::(Poi)·" (Pti)' which is the probability
selecting the ith terminal branch.
It follows that
y. = [(Pl·)···(Pt·)Y
,]+ ...+[(P(k -,·),.,(Pt·)Yk·)+···+[Yt·)
Thus, y. IS the number of fruit "on" the ith terminal branch in-
eluding prorated amounts of path fruit.
Assuming the RP-PPS method
and terminal branch 1-2-1-1 as an example, the value of y. IS
IS .03103 ::::
2379 which gIves
the same result that was obtained when Eq. (3.2) was used.
Table 3.2, columns headed Y2 and Y4' present estimates of
the total number of apples on the tree for the RP-EP and RP-PPS
methods and each of the possible random paths.
were obtained by using the technique of prorating path fruit,
That is, estimat.es of the total number of apples
were obtained by dividing the values of y. (last twO columns of
Table 3.1) by the appropriate probabilities
which are presented
1n Table 3.2, columns P2 and P4.
For comparison of the four methods we now need to decide
how to include the path fruit for the DS-EP and DS-PPS methods.
If the amount of path fruit is small, the best method might be
to count all path fruit at the time the tree is mapped to deter-
mine terminal branches.
In this case, assuming a sample of one
terminal branch, the estimator, would be
is the number of path fruit, y. 1S the number of fruit
on the ith terminal branch and p. is the probability of selecting
the ith terminal branch.
are not considered
illustration because, from a practical viewpoint, interest is in
the random path met