python统计分析电⼦版_⽤Python做统计分析（Scipy.stats的
⽂档）
这个⽂档说了以下内容，对python如何做统计分析感兴趣的⼈可以看看，毕竟Python的库也有点乱。有的看上去应该在⼀起的内容分散在scipy,pandas,sympy等库中。这⾥是⼀般统计功能的使⽤，在scipy库中。像什么时间序列之类的当然在其他地⽅，⽽且它们反过来就没这些功能。
数学高中三角函数公式大全随机变量样本抽取
84个连续性分布(告诉你有那么多，没具体介绍)
12个离散型分布
分布的密度分布函数，累计分布函数，残存函数，分位点函数，逆残存函数
分布的统计量：均值，⽅差，峰度，偏度，矩
分布的线性变换⽣成
insgream官方网下载加速器数据的分布拟合
分布构造
描述统计
t检验，ks检验，卡⽅检验，正态性检，同分布检验
核密度估计(从样本估计概率密度分布函数)
Statistics (scipy.stats)
Introduction
介绍
In this tutorial we discuss many, but certainly not all, features of scipy.stats. The intention here is to provide a user with a working knowledge of this package. We refer to the reference manual for further details.
在这个教程我们讨论⼀些⽽⾮全部的scipy.stats模块的特性。这⾥我们的意图是提供给使⽤者⼀个关于这个包的实⽤性知识。我们推荐reference manual来介绍更多的细节。
Note: This documentation is work in progress.
注意：这个⽂档还在发展中。
Random Variables
随机变量
There are two general distribution classes that have been implemented for encapsulating continuous random variables anddiscrete random variables . Over 80 continuous random variables (RVs) and 10 discrete random variables have been implemented using these classes. Besides this, new routines and distributions can easily added by the end user. (If you create one, please contribute it).
有⼀些通⽤的分布类被封装在continuous random variables以及discrete random variables中。有80多个连续性随机变量(RVs)以及10个离散随机变量已经⽤这些类建⽴。同样，新的程序和分布可以被⽤户新创建(如果你创建了⼀个，请提供它帮助发展这个包)。
All of the statistics functions are located in the sub-package scipy.stats and a fairly complete listing of these functions can be obtained using info(stats). The list of the random variables available can also be obtained from the docstring for the stats sub-package.
所有统计函数被放在⼦包scipy.stats中，且有这些函数的⼀个⼏乎完整的列表可以使⽤info(stats)获得。这个列表⾥的随机变量也可以从stats⼦包的docstring中获得介绍。
In the discussion below we mostly focus on continuous RVs. Nearly all applies to discrete variables also, but we point out some differences here: Specific Points for Discrete Distributions.
在接下来的讨论中，沃恩着重于连续性随机变量(RVs)。⼏乎所有离散变量也符合下⾯的讨论，但是我们也要指出⼀些区别在Specific Points for Discrete Distributions中。
Getting Help
获得帮助
First of all, all distributions are accompanied with help functions. To obtain just some basic information we can call
在开始前，所有分布可以使⽤help函数得到解释。为获得这些信息只需要使⽤简单的调⽤：
>>>
>>> from scipy import stats
>>> from scipy.stats import norm
>>> print norm.__doc__
To find the support, i.e., upper and lower bound of the distribution, call:
为了到⽀持，作为例⼦，我们⽤这种⽅式分布的上下界
>>>
>>> print 'bounds of distribution lower: %s, upper: %s' % (norm.a,norm.b)
随机数生成器怎么弄bounds of distribution lower: -inf, upper: inf
We can list all methods and properties of the distribution with dir(norm). As it turns out, some of the methods are private methods although they are not named as such (their name does not start with a leading underscore), for example veccdf, are only available for internal calculation (those methods will give warnings when one tries to use them, and will be removed at some point).
我们可以通过调⽤dir(norm)来获得关于这个(正态)分布的所有⽅法和属性。应该看到，⼀些⽅法是私
有⽅法尽管其并没有以名称表⽰出来(⽐如它们前⾯没有以下划线开头)，⽐如veccdf就只⽤于内部计算(试图使⽤那些⽅法将引发警告，它们可能会在后续开发中被移除)
To obtain the real main methods, we list the methods of the frozen distribution. (We explain the meaning of a frozen distribution below).
为了获得真正的主要⽅法，我们列举冻结分布的⽅法(我们将在下⽂解释何谓“冻结分布”)
>>>
>>> rv = norm()
>>> dir(rv)  # reformatted
['__class__', '__delattr__', '__dict__', '__doc__', '__getattribute__',
'__hash__', '__init__', '__module__', '__new__', '__reduce__', '__reduce_ex__',
'__repr__', '__setattr__', '__str__', '__weakref__', 'args', 'cdf', 'dist',
'entropy', 'isf', 'kwds', 'moment', 'pdf', 'pmf', 'ppf', 'rvs', 'sf', 'stats']
Finally, we can obtain the list of available distribution through introspection:
最后，我们能通过内省获得所有的可⽤分布。
简易轮播图代码>>>
>>> import warnings
>>> warnings.simplefilter('ignore', DeprecationWarning)
>>> dist_continu = [d for d in dir(stats) if
...                isinstance(getattr(stats,d), stats.rv_continuous)]
>>> dist_discrete = [d for d in dir(stats) if
...                  isinstance(getattr(stats,d), stats.rv_discrete)]
>>> print 'number of continuous distributions:', len(dist_continu)
number of continuous distributions: 84
>>> print 'number of discrete distributions:  ', len(dist_discrete)
number of discrete distributions:  12
Common Methods
通⽤⽅法
The main public methods for continuous RVs are:
连续随机变量的主要公共⽅法如下：
rvs: Random Variates
pdf: Probability Density Function
cdf: Cumulative Distribution Function
sf: Survival Function (1-CDF)
ppf: Percent Point Function (Inverse of CDF)
isf: Inverse Survival Function (Inverse of SF)
stats: Return mean, variance, (Fisher’s) skew, or (Fisher’s) kurtosis  moment: non-central moments of the distribution
rvs：随机变量
pdf：概率密度函。
cdf：累计分布函数
sf：残存函数(1-CDF)
python教程电子版书籍ppf：分位点函数(CDF的逆)
isf：逆残存函数(sf的逆)
stats：返回均值，⽅差，(费舍尔)偏态，(费舍尔)峰度。
moment：分布的⾮中⼼矩。
Let’s take a normal RV as an example.
让我们取得⼀个标准的RV作为例⼦。
>>>
>>> norm.cdf(0)
0.5
To compute the cdf at a number of points, we can pass a list or a numpy array.
为了计算在⼀个点上的cdf，我们可以传递⼀个列表或⼀个numpy数组。
>>>
>>> norm.cdf([-1., 0, 1])
array([ 0.15865525,  0.5      ,  0.84134475])
>>> import numpy as np
>>> norm.cdf(np.array([-1., 0, 1]))
array([ 0.15865525,  0.5      ,  0.84134475])
Thus, the basic methods such as pdf, cdf, and so on are vectorized with np.vectorize.
Other generally useful methods are supported too:
相应的，像pdf,cdf之类的简单⽅法可以被⽮量化通过np.vectorize.
其他游泳的⽅法可以像这样使⽤。
>>>
>>> an(), norm.std(), norm.var()
(0.0, 1.0, 1.0)
>>> norm.stats(moments = "mv")
(array(0.0), array(1.0))
To find the median of a distribution we can use the percent point function ppf, which is the inverse of the cdf：为了到⼀个分部的中⼼，我们可以使⽤分位数函数ppf，其是cdf的逆。
>>>
>>> norm.ppf(0.5)
0.0
To generate a set of random variates:
为了产⽣⼀个随机变量集合。
>>>
>>> norm.rvs(size=5)
array([-0.35687759,  1.34347647, -0.11710531, -1.00725181, -0.51275702])
Don’t think that norm.rvs(5) generates 5 variates:
不要认为norm.rvs(5)产⽣了五个变量。
逻辑算法有哪些>>>
>>> norm.rvs(5)
7.131624370075814
This brings us, in fact, to the topic of the next subsection.
这个引导我们可以得以进⼊下⼀部分的内容。
Shifting and Scaling
位移与缩放(线性变换)
All continuous distributions take loc and scale as keyword parameters to adjust the location and scale of the distribution, e.g. for the standard normal distribution the location is the mean and the scale is the standard deviation.
所有连续分布可以操纵loc以及scale参数作为修正location和scale的⽅式。作为例⼦，标准正态分布的location是均值⽽scale是标准差。
>>>
>>> norm.stats(loc = 3, scale = 4, moments = "mv")
(array(3.0), array(16.0))
In general the standardized distribution for a random variable X is obtained through the transformation (X - loc) / scale. The default values are loc = 0 and scale = 1.
通常经标准化的分布的随机变量X可以通过变换(X-loc)/scale获得。它们的默认值是loc=0以及scale=1.
Smart use of loc and scale can help modify the standard distributions in many ways. To illustrate the scaling further, the cdf of an exponentially distributed RV with mean 1/λ is given by
F(x)=1−exp(−λx)
By applying the scaling rule above, it can be seen that by taking scale  = 1./lambda we get the proper scale.
聪明的使⽤loc与scale可以帮助以灵活的⽅式调整标准分布。为了进⼀步说明缩放的效果，下⾯给出期望为1/λ指数分布的cdf。
F(x)=1−exp(−λx)
通过像上⾯那样使⽤scale，可以看到得到想要的期望值。
>>>
>>> from scipy.stats import expon
>>> an(scale=3.)
3.0
The uniform distribution is also interesting:
均匀分布也是令⼈感兴趣的：
>>>
>>> from scipy.stats import uniform
>>> uniform.cdf([0, 1, 2, 3, 4, 5], loc = 1, scale = 4)
array([ 0.  ,  0.  ,  0.25,  0.5 ,  0.75,  1.  ])
Finally, recall from the previous paragraph that we are left with the problem of the meaning of norm.rvs(5). As it turns out, calling a distribution like this, the first argument, i.e., the 5, gets passed to set the loc parameter. Let’s see:
最后，联系起我们在前⾯段落中留下的norm.rvs(5)的问题。事实上，像这样调⽤⼀个分布，其第⼀个参数，在这⾥是5，是把loc参数调到了5，让我们看：
>>>
>>> np.mean(norm.rvs(5, size=500))

版权声明：本站内容均来自互联网，仅供演示用，请勿用于商业和其他非法用途。如果侵犯了您的权益请与我们联系QQ:729038198，我们将在24小时内删除。