On best fractional linear generating function bounds
- 1 June 1979
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 16 (02) , 449-453
- https://doi.org/10.1017/s0021900200046672
Abstract
Under weak conditions, this paper provides a best lower and a best upper bounding fractional linear generating function for any probability generating function when they have the same mean. These bounds can be used to obtain bounds for the expectation and the percentiles of the extinction-time distribution of a Galton-Watson branching process and other parameters of interest. For the special case of the four points probability generating function, the best bounds obtained are better than the bounds derived by Agresti (1974).Keywords
This publication has 3 references indexed in Scilit:
- Bounds on the extinction time distribution of a branching processAdvances in Applied Probability, 1974
- On asymptotic properties of sub-critical branching processesJournal of the Australian Mathematical Society, 1968
- Inequalities for branching processesJournal of Applied Probability, 1966