更改

Some computing languages provide built-in functions to evaluate the Poisson distribution, namely

Some computing languages provide built-in functions to evaluate the Poisson distribution, namely

* [[R (programming language)|R]]: function <code>dpois(x, lambda)</code>;

* [[R (programming language)|R]]: function <code>dpois(x, lambda)</code>;

=== Generating Poisson-distributed random variables ===

=== Generating Poisson-distributed random variables 生成泊松分布随机变量===

The choice of STEP depends on the threshold of overflow. For double precision floating point format, the threshold is near e⁷⁰⁰, so 500 shall be a safe STEP.

The choice of STEP depends on the threshold of overflow. For double precision floating point format, the threshold is near e⁷⁰⁰, so 500 shall be a safe STEP.

STEP 的选择取决于溢出阈值。对于双精度浮点格式，阈值接近 e < sup > 700 </sup > ，因此500应该是一个安全的 STEP。

STEP 的选择取决于溢出'''<font color="#ff8000"> 阈值Threshold</font>'''。对于双精度浮点格式，'''<font color="#ff8000"> 阈值Threshold</font>'''接近 e < sup > 700 </sup > ，因此500应该是一个安全的 STEP。

Other solutions for large values of λ include rejection sampling and using Gaussian approximation.

Other solutions for large values of λ include rejection sampling and using Gaussian approximation.

Inverse transform sampling is simple and efficient for small values of λ, and requires only one uniform random number u per sample. Cumulative probabilities are examined in turn until one exceeds u.

Inverse transform sampling is simple and efficient for small values of λ, and requires only one uniform random number u per sample. Cumulative probabilities are examined in turn until one exceeds u.

逆变换采样对于小数值的样本是简单有效的，并且每个样本只需要一个均匀的随机数 u。累积概率被依次检查，直到一个超过 u。

逆变换采样对于λ小数值的样本是简单有效的，并且每个样本只需要一个均匀一致的随机数 u。依次检查累积概率，直到其超过 u。

  algorithm Poisson generator based upon the inversion by sequential search:

  algorithm Poisson generator based upon the inversion by sequential search:

基于线性搜索反演的泊松生成算法:

基于顺序检索反演的'''<font color="#ff8000"> 泊松发生器算法Algorithm Poisson generator </font>''':

     '''init''':

     '''init''':

     while u > s do:

     while u > s do:

当你做的时候:

做以下步骤:

         x ← x + 1.

         x ← x + 1.

== History ==

== History历史 ==

The distribution was first introduced by [[Siméon Denis Poisson]] (1781–1840) and published together with his probability theory in his work ''Recherches sur la probabilité des jugements en matière criminelle et en matière civile''(1837).{{r|Poisson1837|p=205-207}} The work theorized about the number of wrongful convictions in a given country by focusing on certain [[random variable]]s ''N'' that count, among other things, the number of discrete occurrences (sometimes called "events" or "arrivals") that take place during a [[time]]-interval of given length. The result had already been given in 1711 by [[Abraham de Moivre]] in ''De Mensura Sortis seu; de Probabilitate Eventuum in Ludis a Casu Fortuito Pendentibus'' .{{r|deMoivre1711|p=219}}{{r|deMoivre1718|p=14-15}}{{r|deMoivre1721|p=193}}{{r|Johnson2005|p=157}} This makes it an example of [[Stigler's law]] and it has prompted some authors to argue that the Poisson distribution should bear the name of de Moivre.{{r|Stigler1982|Hald1984}}

The distribution was first introduced by [[Siméon Denis Poisson]] (1781–1840) and published together with his probability theory in his work ''Recherches sur la probabilité des jugements en matière criminelle et en matière civile''(1837).{{r|Poisson1837|p=205-207}} The work theorized about the number of wrongful convictions in a given country by focusing on certain [[random variable]]s ''N'' that count, among other things, the number of discrete occurrences (sometimes called "events" or "arrivals") that take place during a [[time]]-interval of given length. The result had already been given in 1711 by [[Abraham de Moivre]] in ''De Mensura Sortis seu; de Probabilitate Eventuum in Ludis a Casu Fortuito Pendentibus'' .{{r|deMoivre1711|p=219}}{{r|deMoivre1718|p=14-15}}{{r|deMoivre1721|p=193}}{{r|Johnson2005|p=157}} This makes it an example of [[Stigler's law]] and it has prompted some authors to argue that the Poisson distribution should bear the name of de Moivre.{{r|Stigler1982|Hald1984}}

The distribution was first introduced by Siméon Denis Poisson (1781–1840) and published together with his probability theory in his work Recherches sur la probabilité des jugements en matière criminelle et en matière civile(1837). The work theorized about the number of wrongful convictions in a given country by focusing on certain random variables N that count, among other things, the number of discrete occurrences (sometimes called "events" or "arrivals") that take place during a time-interval of given length. The result had already been given in 1711 by Abraham de Moivre in De Mensura Sortis seu; de Probabilitate Eventuum in Ludis a Casu Fortuito Pendentibus . This makes it an example of Stigler's law and it has prompted some authors to argue that the Poisson distribution should bear the name of de Moivre.

The distribution was first introduced by Siméon Denis Poisson (1781–1840) and published together with his probability theory in his work Recherches sur la probabilité des jugements en matière criminelle et en matière civile(1837). The work theorized about the number of wrongful convictions in a given country by focusing on certain random variables N that count, among other things, the number of discrete occurrences (sometimes called "events" or "arrivals") that take place during a time-interval of given length. The result had already been given in 1711 by Abraham de Moivre in De Mensura Sortis seu; de Probabilitate Eventuum in Ludis a Casu Fortuito Pendentibus . This makes it an example of Stigler's law and it has prompted some authors to argue that the Poisson distribution should bear the name of de Moivre.

The distribution was first introduced by Siméon Denis Poisson (1781–1840) and published together with his probability theory in his work Recherches sur la probabilité des jugements en matière criminelle et en matière civile(1837).这项工作通过关注某些随机变量 n (其中包括在给定时间间隔内发生的离散事件(有时称为“事件”或“到达事件”)的数量)来推断某一国家的错误定罪数量。这个结果早在1711年就已经在《亚伯拉罕·棣莫弗给出了。在 Ludis 举行的猜测活动。这使它成为斯蒂格勒定律的一个例子，并促使一些作者提出，泊松分佈应该以德莫伊弗雷的名字命名。

The distribution was first introduced by Siméon Denis Poisson (1781–1840) and published together with his probability theory in his work Recherches sur la probabilité des jugements en matière criminelle et en matière civile(1837).

这项工作通过关注某些随机变量 n (其中包括在给定时间间隔内发生的离散事件(有时称为“事件”或“到达事件”)的数量)来推断某一国家的错误定罪数量。这个结果早在1711年就已经在《亚伯拉罕·棣莫弗》给出了。在 Ludis 举行的猜测活动。这使它成为斯蒂格勒定律的一个例子，也使一些作者提出，'''<font color="#ff8000"> 泊松分佈Poisson distribution </font>'''应该以德莫伊弗雷的名字命名。

In 1860, Simon Newcomb fitted the Poisson distribution to the number of stars found in a unit of space.

In 1860, Simon Newcomb fitted the Poisson distribution to the number of stars found in a unit of space.

1860年，Simon Newcomb 将泊松分佈天文台与一个空间单位中发现的恒星数量进行了比较。

1860年，Simon Newcomb 将'''<font color="#ff8000"> 泊松分佈Poisson distribution </font>'''与天文台一个空间单位中发现的恒星数量进行了比较。

A further practical application of this distribution was made by [[Ladislaus Bortkiewicz]] in 1898 when he was given the task of investigating the number of soldiers in the Prussian army killed accidentally by horse kicks;{{r|vonBortkiewitsch1898|p=23-25}} this experiment introduced the Poisson distribution to the field of [[reliability engineering]].

A further practical application of this distribution was made by [[Ladislaus Bortkiewicz]] in 1898 when he was given the task of investigating the number of soldiers in the Prussian army killed accidentally by horse kicks;{{r|vonBortkiewitsch1898|p=23-25}} this experiment introduced the Poisson distribution to the field of [[reliability engineering]].

A further practical application of this distribution was made by Ladislaus Bortkiewicz in 1898 when he was given the task of investigating the number of soldiers in the Prussian army killed accidentally by horse kicks; this experiment introduced the Poisson distribution to the field of reliability engineering.

A further practical application of this distribution was made by Ladislaus Bortkiewicz in 1898 when he was given the task of investigating the number of soldiers in the Prussian army killed accidentally by horse kicks; this experiment introduced the Poisson distribution to the field of reliability engineering.

这种分布的进一步实际应用是在1898年，当时拉迪斯劳斯·博特基威茨被赋予调查普鲁士军队中被马踢意外杀死的士兵人数的任务; 这个实验将泊松分佈引入可靠度领域。

这种分布的进一步实际应用是在1898年，当时拉迪斯劳斯·博特基威茨被赋予任务调查普鲁士军队中被马踢意外杀死的士兵人数; 这个实验将'''<font color="#ff8000"> 泊松分佈Poisson distribution </font>'''引入可靠性技术领域。

== See also ==

== See also又及 ==

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=== Sources ===

=== Sources资源 ===

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