The Probability Distribution of Time to Extinction: A simulation study

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The time to extinction (TTE) is very important topic in some fields of studies; ecology, economics, corporate competition, bacterial sciences and epidemiology. The aim of the present paper is to investigate about the empirical parametric and empirical nonparametric probability distribution of the time to extinction for two related stochastic models; Rosenzweig and Macarthur model and May model. First, we assume the amplitude of r is a random variable with a continuous uniform probability distribution on a closed interval [r 1, r 2]. Second, we assume the number of consecutive years’ during which the amplitude of r remains constant is a random variable with a discrete geometric probability distribution with parameter p which is supported on a positive integer ℤ+ and p ∈ (0,1).