The density of the extinction probability of a time homogeneous linear birth and death process under the influence of randomly occurring disasters.
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.
Lee
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Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan. lee@math.nsysu.edu.tw
D001723:Birth Rate; D004190:Disasters / Q000706:statistics & numerical data*; D008954:Models, Biological; D009026:Mortality; D011336:Probability