For faster navigation, this Iframe is preloading the Wikiwand page for
帕累托分布 .
此條目需要擴充。 (2013年11月8日)请協助
改善这篇條目 ,更進一步的信息可能會在
討論頁 或
扩充请求 中找到。请在擴充條目後將此模板移除。
帕累托分布 (Pareto distribution)是以意大利 经济学家维尔弗雷多·帕累托 命名的。 是从大量真实世界的现象中发现的幂定律 分布。这个分布在经济学以外,也被称为布拉德福分布 。
在帕累托分布中,如果X 是一个随机变量 , 则X 的概率分布 如下面的公式所示:
P
(
X
>
x
)
=
(
x
x
min
)
−
k
{\displaystyle {\rm {P))(X>x)=\left({\frac {x}{x_{\min ))}\right)^{-k))
其中x 是任何一个大于x min 的数,x min 是X 最小的可能值(正数),k 是为正的参数。帕累托分布曲线族是由两个数量参数化的:x min 和k 。分布密度则为
p
(
x
)
=
{
0
,
if
x
<
x
min
;
k
x
min
k
x
k
+
1
,
if
x
>
x
min
.
{\displaystyle p(x)=\left\((\begin{matrix}0,&{\mbox{if ))x<x_{\min };\\\\{k\;x_{\min }^{k} \over x^{k+1)),&{\mbox{if ))x>x_{\min }.\end{matrix))\right.}
帕累托分布属于连续概率分布。
“齊夫定律 ”, 也称为“zeta 分布”, 也可以被认为是在离散概率分布中的帕累托分布。 一个遵守帕累托分布的随机变量 的期望值 为
x
min
k
k
−
1
{\displaystyle x_{\min }\;k \over k-1}
(如果
k
≤
1
{\displaystyle k\leq 1}
, 期望值为无穷大) 且随机变量 的标准差 为
x
min
k
−
1
k
k
−
2
{\displaystyle {x_{\min } \over k-1}{\sqrt {k \over k-2))}
(如果
k
≤
2
{\displaystyle k\leq 2}
, 标准差不存在)。
被认为大致是帕累托分布的例子有:
離散單變量
有限支集 無限支集
beta negative binomial
Borel
Conway–Maxwell–Poisson
discrete phase-type
Delaporte
extended negative binomial
Flory–Schulz
Gauss–Kuzmin
幾何分佈
对数分布
mixed Poisson
负二项分布
Panjer
parabolic fractal
卜瓦松分布
Skellam
Yule–Simon
zeta
連續單變量
混合單變量
联合分布
Discrete:
Ewens
multinomial
Continuous:
狄利克雷分布
multivariate Laplace
多元正态分布
multivariate stable
multivariate t
normal-gamma
随机矩阵
LKJ
矩阵正态分布
matrix t
matrix gamma
威沙特分佈
定向統計
循環單變量定向統計
圆均匀分布
univariate von Mises
wrapped normal
wrapped Cauchy
wrapped exponential
wrapped asymmetric Laplace
wrapped Lévy
球形雙變量
Kent
環形雙變量
bivariate von Mises
多變量
von Mises–Fisher
Bingham
退化分布 和奇異分佈 其它
Circular
复合泊松分布
elliptical
exponential
natural exponential
location–scale
Maximum entropy
Mixture
Pearson
Tweedie
Wrapped
{{bottomLinkPreText}}
{{bottomLinkText}}
This page is based on a Wikipedia article written by
contributors (read /edit ).
Text is available under the
CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.
{{current.index+1}} of {{items.length}}
Thanks for reporting this video!
This browser is not supported by Wikiwand :( Wikiwand requires a browser with modern capabilities in order to provide you with the best reading experience. Please download and use one of the following browsers:
An extension you use may be preventing Wikiwand articles from loading properly.
If you're using HTTPS Everywhere or you're unable to access any article on Wikiwand, please consider switching to HTTPS (https ://www.wikiwand.com).
An extension you use may be preventing Wikiwand articles from loading properly.
If you are using an Ad-Blocker , it might have mistakenly blocked our content.
You will need to temporarily disable your Ad-blocker to view this page.
✕
This article was just edited, click to reload
Please click Add in the dialog above
Please click Allow in the top-left corner, then click Install Now in the dialog
Please click Open in the download dialog, then click Install
Please click the "Downloads" icon in the Safari toolbar, open the first download in the list, then click Install
{{::$root.activation.text}}
Follow Us
Don't forget to rate us
Oh no, there's been an error
Please help us solve this error by emailing us at
support@wikiwand.com
Let us know what you've done that caused this error, what browser you're using, and whether you have any special extensions/add-ons installed.
Thank you!