V2EX negative binomial

Negative Binomial

释义 Definition

negative binomial(统计/概率)通常指负二项分布:一种用于描述“在一系列独立伯努利试验中,为得到指定次数的成功所需的失败次数(或试验次数)”的离散概率分布。它也常用于计数数据建模,尤其当数据相对泊松分布表现出过度离散(方差大于均值)时。

发音 Pronunciation (IPA)

/ntv banomil/

例句 Examples

A negative binomial model can fit count data with extra variability.
负二项模型可以拟合具有额外波动性的计数数据。

When the Poisson assumption fails due to overdispersion, researchers often use a negative binomial distribution to model event counts and estimate uncertainty more accurately.
当由于过度离散而不满足泊松假设时,研究者常用负二项分布来建模事件计数,从而更准确地估计不确定性。

词源 Etymology

“binomial(双项式/二项的)”源自拉丁语词根 **bi-**(“二”)+ nomial(与“名称/项”相关,来自 nomen “名字”),在数学中指“由两项组成”或“与二项展开相关”。“negative(负的)”在这里并非“消极”,而是历史上的命名:该分布可看作与二项分布相关一类形式(在某些推导中出现带负号的二项系数/指数推广),因此称为“负二项”。

相关词 Related Words

文学与典籍 Literary Works

  • William Feller, An Introduction to Probability Theory and Its Applications(经典概率论教材中讨论多种离散分布,含负二项分布相关内容)
  • Casella & Berger, Statistical Inference(统计推断教材中涉及分布与参数推断背景下的相关讨论)
  • Gelman et al., Bayesian Data Analysis(在贝叶斯建模的计数数据章节常出现负二项分布/回归)
  • Cameron & Trivedi, Regression Analysis of Count Data(计数数据回归的经典著作,负二项回归是核心模型之一)
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