PubMed · 4121854
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1973-03-24. Britain 2001.. https://pubmed.ncbi.nlm.nih.gov/4121854/
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Under the influence of randomly occurring disasters, the eventual extinction probability, q, of a birth and death process, Z, is a random variable. In this paper, we obtain an integral expression for the probability density function g(x) of q under the assumption that the population process Z is a time homogeneous linear birth and death process and the disasters occur according to an arbitrary renewal process so that its interarrival times have a density. An example is provided to demonstrate how to evaluate the integral numerically.