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ANALYSIS OF PROBABILITY OF ULTIMATE EXTINCTION IN A TIME-INHOMOGENEOUS BRANCHING PROCESS
Keywords:
branching process, time-homogeneity, ultimate extinction, zero offspring, generational.DOI:
https://doi.org/10.17654/0972361722026Abstract
The objective of this paper is to develop a method for analyzing probability of ultimate extinction as well as generational probabilities of zero offspring as proxies for measuring ageing of a given population based on parity data under time-inhomogeneous branching process. This was necessitated by the fact that the time-homogeneous assumption is hardly true in real life situation as corroborated in the paper by statistical hypothesis tests. In the process, a more general theorem, together with some corollaries, based on the ideas of probability generating functions in a branching process, was proposed and successfully proved. The proposed method was applied to both the hypothetical and empirical data and the results were compared with those of the time-homogeneous methods. The results for the two methods were found to be very close for both the hypothetical and the empirical data and hence it was posited that under certain closeness conditions even if the test for time-homogeneity is significant, using the method under the time-homogeneous assumption which is easier, is a step in the right direction, otherwise the proposed method should be used. For the empirical data used, it was also found that, as observed elsewhere, Burkina Faso has the youngest population compared with Colombia and Indonesia.
Received: September 19, 2021
Accepted: October 30, 2021
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