1 results
Polynomial bounds for probability generating functions
-
- Journal:
- Journal of Applied Probability / Volume 12 / Issue 3 / September 1975
- Published online by Cambridge University Press:
- 14 July 2016, pp. 507-514
- Print publication:
- September 1975
-
- Article
- Export citation
-
The problem of approximating an arbitrary probability generating function (p.g.f.)
by a polynomial 
is considered. It is shown that if the coefficients rj are chosen so that LN(·) agrees with g(·) to k derivatives at s = 1 and to (N – k) derivatives at s = 0, then LN is in fact an upper or lower bound to g; the nature of the bound depends only on k and not on N. Application of the results to the problems of finding bounds for extinction probabilities, extinction time distributions and moments of branching process distributions are examined.
by a polynomial 
is considered. It is shown that if the coefficients 