It is shown that the parameter i of the Anton distribution equals the internal rate of return x. In other words it is shown that the root of
is x = i. (A1) results from (3) and (5). (A1) can be rewritten as
Denote
Since (A3) is a geometric series if follows that
provided that 
. Differentiating
(A3) with respect to x gives
On the other hand differentiating (A4) with respect to x gives
Substituting (A8) into (A6), and the result and (A4) into (A2) gives after some algebra
Provided that and 
it follows from (A9) after some
simple, but lengthy algebra that
It is easy to see from (A10) that x = i is the root of equation (A1).
Other roots of equation (A10) are not relevant. It can be proved that no other root exists when N is odd, and that the other root is less than - 1 when N is even.
The next section (Appendix B)
The
previous section (References)
The contents section of Ruuhela, Salmi, Luoma and Laakkonen (1982)
Other scientific publications by Timo Salmi in WWW format
