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此词条暂由水流心不竞初译，未经审校，带来阅读不便，请见谅。

此词条暂由水流心不竞初译，未经审校，带来阅读不便，请见谅。

{{Probability distribution

{{Probability distribution

   | pdf_image  = 325px

   | pdf_image  = 325px

   | pdf_caption = The horizontal axis is the index ''k'', the number of occurrences. ''λ'' is the expected rate of occurrences. The vertical axis is the probability of ''k'' occurrences given ''λ''. The function is defined only at integer values of ''k''; the connecting lines are only guides for the eye.

   | pdf_caption = The horizontal axis is the index ''k'', the number of occurrences. ''λ'' is the expected rate of occurrences. The vertical axis is the probability of ''k'' occurrences given ''λ''. The function is defined only at integer values of ''k''; the connecting lines are only guides for the eye.

   | pdf_caption = The horizontal axis is the index k, the number of occurrences. λ is the expected rate of occurrences. The vertical axis is the probability of k occurrences given λ. The function is defined only at integer values of k; the connecting lines are only guides for the eye.

   | pdf_caption = The horizontal axis is the index k, the number of occurrences. λ is the expected rate of occurrences. The vertical axis is the probability of k occurrences given λ. The function is defined only at integer values of k; the connecting lines are only guides for the eye.

| pdf _ caption = 横轴是索引 k，表示出现的次数。是预期发生率。垂直轴是给定的 k 发生概率。函数只定义在 k 的整数值上，连接线指示方向。

  | pdf _ caption = 横轴是索引 k，表示出现的次数。是预期发生率。垂直轴是给定的 k 发生概率。函数只定义在 k 的整数值上，连接线指示方向。

   | cdf_image  = [[File:poisson cdf.svg|325px]]

   | cdf_image  = [[File:poisson cdf.svg|325px]]

   | cdf_image  = 325px

   | cdf_image  = 325px

   | cdf_caption = The horizontal axis is the index ''k'', the number of occurrences. The CDF is discontinuous at the integers of ''k'' and flat everywhere else because a variable that is Poisson distributed takes on only integer values.

   | cdf_caption = The horizontal axis is the index ''k'', the number of occurrences. The CDF is discontinuous at the integers of ''k'' and flat everywhere else because a variable that is Poisson distributed takes on only integer values.

   | cdf_caption = The horizontal axis is the index k, the number of occurrences. The CDF is discontinuous at the integers of k and flat everywhere else because a variable that is Poisson distributed takes on only integer values.

   | cdf_caption = The horizontal axis is the index k, the number of occurrences. The CDF is discontinuous at the integers of k and flat everywhere else because a variable that is Poisson distributed takes on only integer values.

| cdf _ caption = 水平轴是索引 k，表示出现的次数。因为一个'''<font color="#ff8000"> {泊松分佈 Poisson distribution</font>'''的变量只取整数值，所以 CDF 在 k 的整数和平坦的所有其他地方均不连续。

  | cdf _ caption = 水平轴是索引 k，表示出现的次数。因为一个'''<font color="#ff8000"> {泊松分佈 Poisson distribution</font>'''的变量只取整数值，所以 CDF 在 k 的整数和平坦的所有其他地方均不连续。

   | notation  = <math>\operatorname{Pois}(\lambda)</math>

   | notation  = <math>\operatorname{Pois}(\lambda)</math>

   | notation  = <math>\operatorname{Pois}(\lambda)</math>

   | 表示法 = < math > operatorname { Pois }(lambda) </math >  

 

| 表示法 = < math > operatorname { Pois }(lambda) </math >  

   | parameters = <math>\lambda\in (0, \infty) </math>  (rate)

   | parameters = <math>\lambda\in (0, \infty) </math>  (rate)

   | support    = <math>k \in \mathbb{N}_0</math> ([[Natural numbers]] starting from 0)

   | support    = <math>k \in \mathbb{N}_0</math> ([[Natural numbers]] starting from 0)

   | support    = <math>k \in \mathbb{N}_0</math> (Natural numbers starting from 0)

   | support = < math > k in mathbb { n } _ 0 </math > (自然数从0开始)

 

| support = < math > k in mathbb { n } _ 0 </math > (自然数从0开始)

 

   | pdf        = <math>\frac{\lambda^k e^{-\lambda}}{k!}</math>

   | pdf        = <math>\frac{\lambda^k e^{-\lambda}}{k!}</math>

| pdf = < math > frac { lambda ^ k e ^ {-lambda }{ k！{/math >

  | pdf = < math > frac { lambda ^ k e ^ {-lambda }{ k！{/math >

 

  | cdf        = <math>\frac{\Gamma(\lfloor k+1\rfloor, \lambda)}{\lfloor k\rfloor !}</math>, or <math>e^{-\lambda} \sum_{i=0}^{\lfloor k\rfloor} \frac{\lambda^i}{i!}\ </math>, or <math>Q(\lfloor k+1\rfloor,\lambda)</math>

   | cdf        = <math>\frac{\Gamma(\lfloor k+1\rfloor, \lambda)}{\lfloor k\rfloor !}</math>, or <math>e^{-\lambda} \sum_{i=0}^{\lfloor k\rfloor} \frac{\lambda^i}{i!}\ </math>, or <math>Q(\lfloor k+1\rfloor,\lambda)</math>

   | cdf        = <math>\frac{\Gamma(\lfloor k+1\rfloor, \lambda)}{\lfloor k\rfloor !}</math>, or <math>e^{-\lambda} \sum_{i=0}^{\lfloor k\rfloor} \frac{\lambda^i}{i!}\ </math>, or <math>Q(\lfloor k+1\rfloor,\lambda)</math>

| cdf = < math > frac { Gamma (lfloor k + 1 rfloor，lambda)}{ lfloor k rfloor！{ i = 0}{ lfloor k rfloor } frac { lambda ^ i }{ i！} </math > ，或者 < math > q (lfloor k + 1 rfloor，lambda) </math >  

  | cdf = < math > frac { Gamma (lfloor k + 1 rfloor，lambda)}{ lfloor k rfloor！{ i = 0}{ lfloor k rfloor } frac { lambda ^ i }{ i！} </math > ，或者 < math > q (lfloor k + 1 rfloor，lambda) </math >  

(for <math>k\ge 0</math>, where <math>\Gamma(x, y)</math> is the [[upper incomplete gamma function]], <math>\lfloor k\rfloor</math> is the [[floor function]], and Q is the [[regularized gamma function]])

(for <math>k\ge 0</math>, where <math>\Gamma(x, y)</math> is the [[upper incomplete gamma function]], <math>\lfloor k\rfloor</math> is the [[floor function]], and Q is the [[regularized gamma function]])