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.

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。