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A Stationary Drake Equation Distribution as a Balance of Birth-death Processes
Research Notes of the AAS Pub Date : 2021-03-09 , DOI: 10.3847/2515-5172/abeb7b
David Kipping

Previous critiques of the Drake Equation have highlighted its deterministic nature, implying that the number of civilizations is the same at all times. Here, I build upon earlier work and present a stochastic formulation. The birth of civilizations within the galaxy is modeled as following a uniform rate (Poisson) stochastic process, with a mean rate of λ C . Each then experiences a constant hazard rate of collapse, which defines an exponential distribution with rate parameter λ L . Thus, the galaxy is viewed as a frothing landscape of civilization birth and collapse. Under these assumptions, I show that N in the Drake Equation must follow another Poisson distribution, with a mean rate (λ C /λ L ). This is used to demonstrate why the Copernican Principle does not allow one to infer N, as well evaluating the algebraic probability of being alone in the galaxy.



中文翻译:

作为生死过程平衡的平稳德雷克方程分布

先前对德雷克方程的批评强调了它的确定性,暗示文明的数量在任何时候都是相同的。在这里,我在早期工作的基础上提出了一个随机公式。银河系内文明的诞生被建模为遵循均匀速率(泊松)随机过程,平均速率为λ C。然后,每个人都会经历一个恒定的坍塌危险率,这定义了一个指数分布,其速率参数为 λ L。因此,银河系被视为文明诞生和崩溃的泡沫景观。在这些假设下,我表明Drake 方程中的N必须遵循另一个泊松分布,平均速率 ( λ C / λ L )。这用于证明为什么哥白尼原理不允许人们推断N,以及评估独自在银河系中的代数概率。

更新日期:2021-03-09
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