现实中常见的概率分布

现实世界中实际观测数据常见的概率分布：正态分布、帕累托分布、极值分布、稳定分布、均匀分布。

一、正态分布、帕累托分布

https://www.zhihu.com/question/20849901

https://www.statisticshowto.datasciencecentral.com/probability-and-statistics/normal-distributions/

https://www.statisticshowto.datasciencecentral.com/pareto-distribution/

   帕累托分布（Pareto distribution）和高斯分布（Gaussian Distribution；正态分布，normal distribution）并列为两大主导自然和人类现象的概率分布。

   高斯分布的本质是独立性 (independence)。大量同质独立事件将导致高斯分布 (由大数定律保证)。

   帕累托分布的本质是正反馈机制（positive feedback loop）。当事件不再独立（a. 事件之间通信成本降低; b. 事件之间的作用力增强 [1]），一个事件的产生对自身和其它同质事件的产生发生影响时，会导致帕累托分布。

   [1] Pierpaolo Andriani, Bill McKelvey. Perspective—From Gaussian to Paretian Thinking: Causes and Implications of Power Laws in Organizations[J]. ORGANIZATION SCIENCE, 2009, 20(6): 1053-1071.

https://pubsonline.informs.org/doi/abs/10.1287/orsc.1090.0481

二、极值分布 Extreme value distributions

   极值分布（extreme value distributions）是指在概率论中极大值（或者极小值）的概率分布。

   极值分布分为第Ⅰ、Ⅱ、Ⅲ 型极值分布，也分别称为 Gumbel、Fréchet、Weibull 型极值分布。

https://baike.baidu.com/item/%E6%9E%81%E5%80%BC%E5%88%86%E5%B8%83

https://www.statisticshowto.datasciencecentral.com/extreme-value-distribution/

https://mathworld.wolfram.com/ExtremeValueDistribution.html

   EVD Type I: Gumbel Distribution (also called the Gumbel-Type). This is the most common EVD and has two forms: one for the minimum, and one for the maximum,

https://www.statisticshowto.datasciencecentral.com/gumbel-distribution/

   EVD Type II: Fréchet Distribution. This distribution is used to model maximum values in a data set .

https://www.statisticshowto.datasciencecentral.com/frechet-distribution/

   EVD Type III: Weibull Distribution . The Weibull distribution is used in assessing product reliability to model failure times and life data analysis

https://www.statisticshowto.datasciencecentral.com/weibull-distribution/

   广义极值分布, The Generalized Extreme Value Distribution,  Fisher–Tippett distribution

https://www.statisticshowto.datasciencecentral.com/extreme-value-distribution/

三、威布尔分布 Weibull distribution

https://www.statisticshowto.datasciencecentral.com/weibull-distribution/

Statistics How To

   The Weibull distributions above include two exponential distributions (top row), a right-skewed distribution (bottom left) and a symmetric distribution (bottom right). The exponential distribution is a special case of the Weibull distribution, which happens when the Weibull shape parameter equals 1.

   Exponential distribution （Poisson Process）

https://www.statisticshowto.datasciencecentral.com/exponential-distribution/

四、稳定分布 Stable distribution

   Stable distributions are a general family of probabilities distributions that share certain properties. They were first described by Paul Lévy (1925) and so are also sometimes informally called Lévy distributions.

https://www.encyclopediaofmath.org/index.php/Stable_distribution

https://www.statisticshowto.datasciencecentral.com/stable-distribution/

   幂律分布

http://wiki.swarma.net/index.php/%E5%B9%82%E5%BE%8B%E5%88%86%E5%B8%83

   稳定分布与广义中心极限定理

http://www.swarmagents.cn/bs/membership/viewelite.asp?id=16660&user=jake&elite=1

五、均匀分布 Uniform distribution

https://www.britannica.com/topic/uniform-distribution-statistics

https://mathworld.wolfram.com/UniformDistribution.html

https://www.investopedia.com/terms/u/uniform-distribution.asp

   Uniform Distribution / Rectangular Distribution: What is it? 

https://www.statisticshowto.datasciencecentral.com/uniform-distribution/

六、感谢杨立坚老师推荐 Geometric Distribution、Negative Binomial；Distribution；F distribution；t Distribution；Kolmogorov Distribution

http://blog.sciencenet.cn/blog-941132-1224413.html

6.1.  几何分布 Geometric Distribution
   Geometric Distribution
The geometric distribution represents the number of failures before you get a success in a series of Bernoulli trials.
https://mathworld.wolfram.com/GeometricDistribution.html
https://www.encyclopediaofmath.org/index.php/Geometric_distribution
          
6.2.  负二项分布 Negative Binomial Distribution
   The negative binomial distribution, also known as the Pascal distribution or Pólya distribution
https://mathworld.wolfram.com/NegativeBinomialDistribution.html
https://www.encyclopediaofmath.org/index.php/Negative_binomial_distribution
https://www.statisticshowto.datasciencecentral.com/?s=Negative+Binomial+Distribution
    
6.3.  F分布 F distribution
   A continuous statistical distribution which arises in the testing of whether two observed samples have the same variance.
https://mathworld.wolfram.com/F-Distribution.html
http://socr.ucla.edu/Applets.dir/F_Table.html
https://courses.lumenlearning.com/introstats1/chapter/facts-about-the-f-distribution/
     
6.4.  t-分布 t Distribution
   A statistical distribution published by William Gosset in 1908. His employer, Guinness Breweries, required him to publish under a pseudonym, so he chose "Student."
https://mathworld.wolfram.com/Studentst-Distribution.html
https://www.statisticshowto.datasciencecentral.com/probability-and-statistics/t-distribution/
https://www.encyclopediaofmath.org/index.php/Student_test
        
6.5.  柯尔莫哥罗夫-斯米诺夫分布系 Kolmogorov Distribution
   A goodness-of-fit test for any statistical distribution. The test relies on the fact that the value of the sample cumulative density function is asymptotically normally distributed.
https://mathworld.wolfram.com/Kolmogorov-SmirnovTest.html
https://www.statisticshowto.datasciencecentral.com/probability-and-statistics/t-distribution/
https://www.encyclopediaofmath.org/index.php/Kolmogorov-Smirnov_test
https://www.math.ucla.edu/~tom/distributions/Kolmogorov.html

   好像网站《Statistics How To: Elementary Statistics for the rest of us!》很不错！

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