V2EX empirical distribution

Empirical Distribution

释义 / Definition

经验分布(empirical distribution):由样本数据直接构造出来的分布,用来描述“在这组观测中各个取值出现的频率/比例”。常见形式包括经验分布函数(EDF)、样本频率表、直方图等。它是对真实但未知的“总体分布”的一种数据驱动近似。

发音 / Pronunciation (IPA)

/mprkl dstrbjun/

例句 / Examples

The empirical distribution shows that most values cluster around 10.
经验分布显示大多数数值集中在 10 附近。

Using the empirical distribution function, we can compare the sample to a theoretical normal distribution and quantify the difference.
利用经验分布函数,我们可以将样本与理论正态分布进行比较,并量化它们的差异。

词源 / Etymology

empirical 来自希腊语 empeirikos(意为“凭经验的、基于观察的”),强调“从数据/经验出发”;distribution 源自拉丁语 distribuere(分开分配),在统计学中指“数值如何在范围内分布”。合起来即“由观测数据得到的分布”。

文献与作品中的用例 / Notable Works

  • Larry Wasserman, All of Statistics: A Concise Course in Statistical Inference(讨论经验分布/经验分布函数与推断的基础联系)
  • Trevor Hastie, Robert Tibshirani, Jerome Friedman, The Elements of Statistical Learning(在非参数方法与密度估计语境中涉及经验分布思想)
  • David Freedman, Robert Pisani, Roger Purves, Statistics(以直观方式介绍基于样本的分布刻画)
  • Michael J. Evans & Jeffrey S. Rosenthal, Probability and Statistics: The Science of Uncertainty(用经验分布连接样本与理论分布)
  • Peter J. Bickel & Kjell A. Doksum, Mathematical Statistics: Basic Ideas and Selected Topics(在理论统计框架中使用经验分布/EDF)
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