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负二项式分布计算器

结果：

负二项分布是统计学上一种离散概率分布。满足以下条件的称为负二项分布：实验包含一系列独立的实验， 每个实验都有成功、失败两种结果，成功的概率是恒定的，实验持续到r次成功，r为正整数。

满足以下条件的称为负二项分布：1. 实验包含一系列独立的实验。2. 每个实验都有成功、失败两种结果。3. 成功的概率是恒定的。4. 实验持续到r次成功，r为正整数。

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负二项分布计算器

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最后更新： · 公式与示例已人工校对

负二项分布回答的问题是：要取得 r 次成功，需要经历多少次失败。它与二项分布方向相反：二项分布固定试验次数看成功几次，负二项分布固定成功次数看要试多少次。适用于重复试验直到达成目标的场景。

使用方法

  1. 填入成功次数 r 与单次成功概率 p
  2. 填入关注的失败次数 k
  3. 点击计算得到对应概率

计算公式

概率质量函数 P(X=k) = C(k+r−1, k) · p^r · (1−p)^k k 为失败次数
期望失败次数 E(X) = r(1−p) / p 达到 r 次成功前平均失败数
总试验次数期望 r / p 含成功与失败

计算示例

投篮命中率 40%，要投中 3 球，恰好失手 2 次的概率
  1. r = 3，p = 0.4，k = 2
  2. 组合数 C(4,2) = 6
  3. 成功项 0.4³ = 0.064
  4. 失败项 0.6² = 0.36
  5. 相乘：6 × 0.064 × 0.36 ≈ 0.1382，即约 13.8%
结果：约 13.8%

要点与常见误区

常见问题

负二项分布和二项分布的区别在哪
二项分布是「做 n 次试验，成功几次」，试验次数固定。负二项分布是「成功 r 次就停，总共做了几次」，成功次数固定。前者问结果分布，后者问耗时分布。
为什么又叫帕斯卡分布
因为帕斯卡最早研究了这个概率问题，特指 r 为整数时的情形。当 r 取实数时它成为更一般的分布族，在过度离散的计数数据建模中被广泛使用。

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Negative Binomial Distribution Calculator is an online statistics tool for data analysis programmed to find out the discrete probability distribution of number of failures that occurs at the beginning of the sequence until the given number of successes to be achieved

Definition

The Negative Binomial is a discrete probability function also known as the Pascal or Polya distribution, used for analysis of count data and offers probability for integer values from 0 to infinity. Negative Binomial is similar to Bernoulli trials. The difference is that the Bernoulli trials represents the number of successes, while the Negative Binomial represents the number of failures that occurs at the beginning of the sequence until the given number of successes to be achieved. It differs from the Poisson distribution which allows for the conditional variations to exceed the conditional mean. The negative binomial distribution is the end result of a process which begins with a Poisson distribution with mean
The collection of tools employs the study of methods and procedures used for gathering, organizing, and analyzing data to understand theory of Probability and Statistics. The set of ideas which is intended to offer the way for making scientific implication from such resulting summarized data. In many applications it is necessary to calculate the Negative Binomial Distribution. With this online Negative Binomial Distribution calculator you can effortlessly make your calculation for a respective input data

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