查看“︁歐文–賀爾分佈”︁的源代码

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{| class="infobox bordered" style="width: 325px; max-width: 325px; font-size: 95%; text-align: left; margin-bottom: 10px;"
|+ 歐文–賀爾分佈
| colspan="2" | 累積分佈函數 <br>
[[File:Irwin-hall-cdf.svg|276x276像素|Cumulative distribution function for the distribution]]
|-
! 參數
| <math>n\in</math> [[自然数|<math>\mathbb N_0</math>]]
|-
! <span class="ilh-all"><span class="ilh-page">支撐集</span><span class="noprint ilh-comment">（<span class="ilh-lang">[[汉语|中文]]</span><span class="ilh-colon">：</span><span class="ilh-link">[//zh.wikipedia.org/wiki/支撐集 <span dir="auto" lang="zh">支撐集</span>]</span>）</span></span><span class="ilh-all"></span>
| <math>x \in [0,n]</math>
|-
! <span class="ilh-all"><span class="ilh-page">概率密度函數</span><span class="noprint ilh-comment">（<span class="ilh-lang">[[汉语|中文]]</span><span class="ilh-colon">：</span><span class="ilh-link">[//zh.wikipedia.org/wiki/概率密度函數 <span dir="auto" lang="zh">概率密度函數</span>]</span>）</span></span><span class="ilh-all"></span>
| <math>\frac{1}{(n-1)!}\sum_{k=0}^{\lfloor x\rfloor}(-1)^k\binom{n}{k}(x-k)^{n-1}</math>
|-
! [[累积分布函数|累積分佈函數]]
| <math>\frac{1}{n!}\sum_{k=0}^{\lfloor x\rfloor}(-1)^k\binom{n}{k}(x-k)^n</math>
|-
! [[期望值]]
| <math>\frac{n}{2}</math>
|-
! <span class="ilh-all"><span class="ilh-page">[[中位數]]</span><span class="noprint ilh-comment">（<span class="ilh-lang">[[汉语|中文]]</span><span class="ilh-colon">：</span><span class="ilh-link">[//zh.wikipedia.org/wiki/中位數 <span dir="auto" lang="zh">中位數</span>]</span>）</span></span><span class="ilh-all"></span>
| <math>\frac{n}{2}</math>
|-
! <span class="ilh-all"><span class="ilh-page">[[众数 (数学)|眾數]]</span><span class="noprint ilh-comment">（<span class="ilh-lang">[[汉语|中文]]</span><span class="ilh-colon">：</span><span class="ilh-link">[//zh.wikipedia.org/wiki/眾數 <span dir="auto" lang="zh">眾數</span>]</span>）</span></span><span class="ilh-all"></span>
|<math>[0,1]</math>里面任意值（<math>n=1</math>）

<math>\frac n2</math>（其它情況）
|-
! <span class="ilh-all"><span class="ilh-page">方差</span><span class="noprint ilh-comment">（<span class="ilh-lang">[[汉语|中文]]</span><span class="ilh-colon">：</span><span class="ilh-link">[//zh.wikipedia.org/wiki/方差 <span dir="auto" lang="zh">方差</span>]</span>）</span></span><span class="ilh-all"></span>
| <math>\frac{n}{12}</math>
|-
!      <span class="ilh-all"><span class="ilh-page">偏度</span><span class="noprint ilh-comment">（<span class="ilh-lang">[[汉语|中文]]</span><span class="ilh-colon">：</span><span class="ilh-link">[//zh.wikipedia.org/wiki/偏度 <span dir="auto" lang="zh">偏度</span>]</span>）</span></span><span class="ilh-all"></span>
|  0
|-
!      <span class="ilh-all"><span class="ilh-page">峰度</span><span class="noprint ilh-comment">（<span class="ilh-lang">[[汉语|中文]]</span><span class="ilh-colon">：</span><span class="ilh-link">[//zh.wikipedia.org/wiki/峰度 <span dir="auto" lang="zh">峰度</span>]</span>）</span></span><span class="ilh-all"></span>
|  <math>-\tfrac{6}{5n}</math>
|-
! [[動差生成函數|矩生成函數]]
| <math>{\left(\frac{\mathrm{e}^{t}-1}{t}\right)}^n</math>
|-
! <span class="ilh-all"><span class="ilh-page">特徵函數</span><span class="noprint ilh-comment">（<span class="ilh-lang">[[汉语|中文]]</span><span class="ilh-colon">：</span><span class="ilh-link">[//zh.wikipedia.org/wiki/特徵函數&#x20;(概率論) <span dir="auto" lang="zh">特徵函數 (概率論)</span>]</span>）</span></span><span class="ilh-all"></span>
| <math>{\left(\frac{\mathrm{e}^{it}-1}{it}\right)}^n</math>
|}
'''歐文–賀爾分佈'''（{{Lang-en|'''Irwin–Hall distribution'''}}）是一種<span class="ilh-all"><span class="ilh-page">概率分佈</span><span class="noprint ilh-comment">（<span class="ilh-lang">[[汉语|中文]]</span><span class="ilh-colon">：</span><span class="ilh-link">[//zh.wikipedia.org/wiki/概率分佈 <span dir="auto" lang="zh">概率分佈</span>]</span>）</span></span>，<math>n</math>個服從區間<math>[0,1]</math>上面的[[均勻分佈]]的<span class="ilh-all"><span class="ilh-page">隨機變量</span><span class="noprint ilh-comment">（<span class="ilh-lang">[[汉语|中文]]</span><span class="ilh-colon">：</span><span class="ilh-link">[//zh.wikipedia.org/wiki/隨機變量 <span dir="auto" lang="zh">隨機變量</span>]</span>）</span></span>的總和服從參數為<math>n</math>的歐文–賀爾分佈。

== 應用 ==
在[[计算机科学]]中，將12個服從均勻分佈的[[隨機數]]相加可以產生服從參數為12的歐文–賀爾分佈的隨機數，再減6，就得到近似服從<span class="ilh-all"><span class="ilh-page">標準正態分佈</span><span class="noprint ilh-comment">（<span class="ilh-lang">[[汉语|中文]]</span><span class="ilh-colon">：</span><span class="ilh-link">[//zh.wikipedia.org/wiki/正態分佈 <span dir="auto" lang="zh">正態分佈</span>]</span>）</span></span><span class="ilh-all"></span>的隨機數。这个是從均勻分佈隨機數產生正態分佈隨機數的一種常用方法。

{{概率分布}}

[[Category:概率论]]
[[Category:數學小作品]]