Computational Probability. The Proceedings of the Actuarial by P. M. Kahn

By P. M. Kahn

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Extra resources for Computational Probability. The Proceedings of the Actuarial Research Conference on Computational Probability Held at Brown University, Providence, Rhode Island, on August 28–30, 1975

Example text

It is advisable COMPUTATIONAL PROBLEMS RELATED TO THE GAL TON-WA TSON PROCESS 33 to compute p0 separately and to a high accuracy. If the value of p0 is essentially correct, we may use the normalizing condition Spk = 1, to determine the number of generations needed in (66) to obtain the probabilities pk, k > 1, to a sufficient degree of accuracy. The computation of the density {7[k} is of interest in the numerical investigation of the priority rules discussed by Nair and Neuts [5,6]. 4. THE MACIMUM GENERATION SIZE BEFORE EXTINCTION The random variable U = max{Xn, n > 0} of the successive - generation sizes before extinction in a Galton-Watson process has been discussed by J.

One could go on, and consider (as Kendall did) married and single people separately. This would give rise to a trivariate process. One could go further and introduce social groups with differing birth and death rates. However the crucial feature in the case of human (indeed most animal) populations is the dependence of fertility and to a lesser extent mortality on age, and this is a major drawback in the above type of model for population growth. It would probably be better to test the validity and relevance of these models for particular scientific applications before developing the theory much further.

Moreover the computed distributions are defective. e > e}, max {i: I (j-i+1)0) j>i 1 1, implement the recurrence relations (34) with N = 12(n). ,0 (39) i=N 2(n) and implement (34) with N = 12(n). This method has the advantage that no probability is "lost" in the recursive computation in the sense that for all n > 0, we have that N ~0(n) + S ' (i)() (40) e = 1.

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