V2EX poisson process

Poisson Process

释义 Definition

泊松过程:一种常见的随机过程/计数过程,用来描述“事件在时间(或空间)中随机发生”的情形。其典型特征是:在任意时间长度为 \(t\) 的区间内发生的事件数服从泊松分布,不同不重叠区间的增量相互独立;在“齐次(homogeneous)”情形下,平均发生率为常数 \(\lambda\),相邻两次事件的间隔时间服从指数分布
(在更广义的“非齐次”版本中,发生率可随时间变化。)

发音 Pronunciation (IPA)

/pwsn prss/

例句 Examples

Customer arrivals at the café are often modeled as a Poisson process.
咖啡馆的顾客到达常常被建模为一个泊松过程。

Assuming a homogeneous Poisson process with rate λ, the number of events in time t follows a Poisson(λt) distribution.
假设事件以强度为 λ 的齐次泊松过程发生,那么在时间 t 内的事件数服从 Poisson(λt) 分布。

词源 Etymology

Poisson 来自法国数学家 西蒙德尼泊松(Siméon Denis Poisson) 的姓氏,相关分布与过程以其研究而得名;process 源自拉丁语 processus,意为“推进、过程”,在数学中指“随时间演化的一类量/现象”。

相关词 Related Words

文学与典籍中的用例 Literary Works

  • An Introduction to Probability Theory and Its Applications(William Feller)
  • Introduction to Probability Models(Sheldon M. Ross)
  • Stochastic Processes(J. L. Doob)
  • Queueing Systems(Leonard Kleinrock)
  • Recherches sur la probabilité des jugements en matière criminelle et en matière civile(S. D. Poisson,1837;与“泊松”相关思想的经典来源之一)
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