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Pandas高级教程之:统计方法
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数据分析中经常会用到很多统计类的方法，本文将会介绍Pandas中使用到的统计方法。
变动百分百
Series和DF都有一个pct_change() 方法用来计算数据变动的百分比。这个方法在填充NaN值的时候特别有用。
ser = pd.Series(np.random.randn(8))
ser.pct_change()
Out[45]:
0 NaN
1 -1.264716
2 4.125006
3 -1.159092
4 -0.091292
5 4.837752
6 -1.182146
7 -8.721482
dtype: float64
ser
Out[46]:
0 -0.950515
1 0.251617
2 1.289537
3 -0.205155
4 -0.186426
5 -1.088310
6 0.198231
7 -1.530635
dtype: float64
pct_change还有个periods参数，可以指定计算百分比的periods，也就是隔多少个元素来计算：
In [3]: df = pd.DataFrame(np.random.randn(10, 4))
In [4]: df.pct_change(periods=3)
Out[4]:
0 1 2 3
0 NaN NaN NaN NaN
1 NaN NaN NaN NaN
2 NaN NaN NaN NaN
3 -0.218320 -1.054001 1.987147 -0.510183
4 -0.439121 -1.816454 0.649715 -4.822809
5 -0.127833 -3.042065 -5.866604 -1.776977
6 -2.596833 -1.959538 -2.111697 -3.798900
7 -0.117826 -2.169058 0.036094 -0.067696
8 2.492606 -1.357320 -1.205802 -1.558697
9 -1.012977 2.324558 -1.003744 -0.371806
Covariance协方差
Series.cov() 用来计算两个Series的协方差，会忽略掉NaN的数据。
In [5]: s1 = pd.Series(np.random.randn(1000))
In [6]: s2 = pd.Series(np.random.randn(1000))
In [7]: s1.cov(s2)
Out[7]: 0.0006801088174310875
同样的，DataFrame.cov() 会计算对应Series的协方差，也会忽略NaN的数据。
In [8]: frame = pd.DataFrame(np.random.randn(1000, 5), columns=["a", "b", "c", "d", "e"])
In [9]: frame.cov()
Out[9]:
a b c d e
a 1.000882 -0.003177 -0.002698 -0.006889 0.031912
b -0.003177 1.024721 0.000191 0.009212 0.000857
c -0.002698 0.000191 0.950735 -0.031743 -0.005087
d -0.006889 0.009212 -0.031743 1.002983 -0.047952
e 0.031912 0.000857 -0.005087 -0.047952 1.042487
DataFrame.cov 带有一个min_periods参数，可以指定计算协方差的最小元素个数，以保证不会出现极值数据的情况。
In [10]: frame = pd.DataFrame(np.random.randn(20, 3), columns=["a", "b", "c"])
In [11]: frame.loc[frame.index[:5], "a"] = np.nan
In [12]: frame.loc[frame.index[5:10], "b"] = np.nan
In [13]: frame.cov()
Out[13]:
a b c
a 1.123670 -0.412851 0.018169
b -0.412851 1.154141 0.305260
c 0.018169 0.305260 1.301149
In [14]: frame.cov(min_periods=12)
Out[14]:
a b c
a 1.123670 NaN 0.018169
b NaN 1.154141 0.305260
c 0.018169 0.305260 1.301149
Correlation相关系数
corr() 方法可以用来计算相关系数。有三种相关系数的计算方法：
方法名 描述pearson (default)
标准相关系数
kendall
Kendall Tau相关系数
spearman
斯皮尔曼等级相关系数
n [15]: frame = pd.DataFrame(np.random.randn(1000, 5), columns=["a", "b", "c", "d", "e"])
In [16]: frame.iloc[::2] = np.nan
# Series with Series
In [17]: frame["a"].corr(frame["b"])
Out[17]: 0.013479040400098775
In [18]: frame["a"].corr(frame["b"], method="spearman")
Out[18]: -0.007289885159540637
# Pairwise correlation of DataFrame columns
In [19]: frame.corr()
Out[19]:
a b c d e
a 1.000000 0.013479 -0.049269 -0.042239 -0.028525
b 0.013479 1.000000 -0.020433 -0.011139 0.005654
c -0.049269 -0.020433 1.000000 0.018587 -0.054269
d -0.042239 -0.011139 0.018587 1.000000 -0.017060
e -0.028525 0.005654 -0.054269 -0.017060 1.000000
corr同样也支持 min_periods ：
In [20]: frame = pd.DataFrame(np.random.randn(20, 3), columns=["a", "b", "c"])
In [21]: frame.loc[frame.index[:5], "a"] = np.nan
In [22]: frame.loc[frame.index[5:10], "b"] = np.nan
In [23]: frame.corr()
Out[23]:
a b c
a 1.000000 -0.121111 0.069544
b -0.121111 1.000000 0.051742
c 0.069544 0.051742 1.000000
In [24]: frame.corr(min_periods=12)
Out[24]:
a b c
a 1.000000 NaN 0.069544
b NaN 1.000000 0.051742
c 0.069544 0.051742 1.000000
corrwith 可以计算不同DF间的相关系数。
In [27]: index = ["a", "b", "c", "d", "e"]
In [28]: columns = ["one", "two", "three", "four"]
In [29]: df1 = pd.DataFrame(np.random.randn(5, 4), index=index, columns=columns)
In [30]: df2 = pd.DataFrame(np.random.randn(4, 4), index=index[:4], columns=columns)
In [31]: df1.corrwith(df2)
Out[31]:
one -0.125501
two -0.493244
three 0.344056
four 0.004183
dtype: float64
In [32]: df2.corrwith(df1, axis=1)
Out[32]:
a -0.675817
b 0.458296
c 0.190809
d -0.186275
e NaN
dtype: float64
rank等级
rank方法可以对Series中的数据进行排列等级。什么叫等级呢？ 我们举个例子：
s = pd.Series(np.random.randn(5), index=list("abcde"))
s
Out[51]:
a 0.336259
b 1.073116
c -0.402291
d 0.624186
e -0.422478
dtype: float64
s["d"] = s["b"] # so there's a tie
s
Out[53]:
a 0.336259
b 1.073116
c -0.402291
d 1.073116
e -0.422478
dtype: float64
s.rank()
Out[54]:
a 3.0
b 4.5
c 2.0
d 4.5
e 1.0
dtype: float64
上面我们创建了一个Series，里面的数据从小到大排序 ：
-0.422478 < -0.402291 < 0.336259 < 1.073116 < 1.073116
所以相应的rank就是 1 ， 2 ，3 ，4 ， 5.
因为我们有两个值是相同的，默认情况下会取两者的平均值，也就是 4.5.
除了 default_rank ， 还可以指定max_rank ，这样每个值都是最大的5 。
还可以指定 NA_bottom ， 表示对于NaN的数据也用来计算rank，并且会放在最底部，也就是最大值。
还可以指定 pct_rank ， rank值是一个百分比值。
df = pd.DataFrame(data={'Animal': ['cat', 'penguin', 'dog',
... 'spider', 'snake'],
... 'Number_legs': [4, 2, 4, 8, np.nan]})
>>> df
Animal Number_legs
0 cat 4.0
1 penguin 2.0
2 dog 4.0
3 spider 8.0
4 snake NaN
df['default_rank'] = df['Number_legs'].rank()
>>> df['max_rank'] = df['Number_legs'].rank(method='max')
>>> df['NA_bottom'] = df['Number_legs'].rank(na_option='bottom')
>>> df['pct_rank'] = df['Number_legs'].rank(pct=True)
>>> df
Animal Number_legs default_rank max_rank NA_bottom pct_rank
0 cat 4.0 2.5 3.0 2.5 0.625
1 penguin 2.0 1.0 1.0 1.0 0.250
2 dog 4.0 2.5 3.0 2.5 0.625
3 spider 8.0 4.0 4.0 4.0 1.000
4 snake NaN NaN NaN 5.0 NaN
rank还可以指定按行 (axis=0) 或者 按列 (axis=1)来计算。
In [36]: df = pd.DataFrame(np.random.randn(10, 6))
In [37]: df[4] = df[2][:5] # some ties
In [38]: df
Out[38]:
0 1 2 3 4 5
0 -0.904948 -1.163537 -1.457187 0.135463 -1.457187 0.294650
1 -0.976288 -0.244652 -0.748406 -0.999601 -0.748406 -0.800809
2 0.401965 1.460840 1.256057 1.308127 1.256057 0.876004
3 0.205954 0.369552 -0.669304 0.038378 -0.669304 1.140296
4 -0.477586 -0.730705 -1.129149 -0.601463 -1.129149 -0.211196
5 -1.092970 -0.689246 0.908114 0.204848 NaN 0.463347
6 0.376892 0.959292 0.095572 -0.593740 NaN -0.069180
7 -1.002601 1.957794 -0.120708 0.094214 NaN -1.467422
8 -0.547231 0.664402 -0.519424 -0.073254 NaN -1.263544
9 -0.250277 -0.237428 -1.056443 0.419477 NaN 1.375064
In [39]: df.rank(1)
Out[39]:
0 1 2 3 4 5
0 4.0 3.0 1.5 5.0 1.5 6.0
1 2.0 6.0 4.5 1.0 4.5 3.0
2 1.0 6.0 3.5 5.0 3.5 2.0
3 4.0 5.0 1.5 3.0 1.5 6.0
4 5.0 3.0 1.5 4.0 1.5 6.0
5 1.0 2.0 5.0 3.0 NaN 4.0
6 4.0 5.0 3.0 1.0 NaN 2.0
7 2.0 5.0 3.0 4.0 NaN 1.0
8 2.0 5.0 3.0 4.0 NaN 1.0
9 2.0 3.0 1.0 4.0 NaN 5.0
本文已收录于 http://www.flydean.com/10-python-pandas-statistical/
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