V2EX bernoulli distribution

Bernoulli Distribution

释义 Definition

伯努利分布:一种最基本的离散概率分布,用来描述只有两种结果的随机试验(通常记为成功/失败、1/0)。若成功的概率为 p,则随机变量 \(X\in\{0,1\}\),且
\(P(X=1)=p,\; P(X=0)=1-p\)。
(它是二项分布在试验次数 \(n=1\) 时的特例。)

发音 Pronunciation (IPA)

/brnuli dstrbjun/

例句 Examples

A coin flip can be modeled with a Bernoulli distribution.
抛硬币可以用伯努利分布来建模。

In machine learning, we often assume each label is a Bernoulli distribution with parameter \(p\), then estimate \(p\) from data.
在机器学习中,我们常把每个标签看作参数为 \(p\) 的伯努利分布,然后用数据去估计 \(p\)。

词源 Etymology

“Bernoulli” 来自瑞士数学家雅各布伯努利(Jacob Bernoulli)的姓氏;“distribution”意为“分布”。伯努利家族在概率论与数学分析的发展中贡献很大,因此许多概念以其命名(如伯努利试验、伯努利数等)。

相关词 Related Words

文学与经典著作 Literary Works

  • An Introduction to Probability Theory and Its Applications William Feller(讨论伯努利试验与相关分布)
  • Introduction to Probability Dimitri P. Bertsekas & John N. Tsitsiklis(以伯努利分布作为离散分布入门例子)
  • All of Statistics: A Concise Course in Statistical Inference Larry Wasserman(在统计推断与二项/伯努利模型中多次出现)
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