NumPy - 统计函数

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NumPy 有许多有用的统计函数，用于从数组中给定的元素中查找最小值、最大值、百分位数、标准差和方差等。这些函数解释如下：

numpy.amin() 和 numpy.amax()

这些函数返回给定数组中沿指定轴的元素的最小值和最大值。

示例

import numpy as np 
a = np.array([[3,7,5],[8,4,3],[2,4,9]]) 

print 'Our array is:' 
print a  
print '\n'  

print 'Applying amin() function:' 
print np.amin(a,1) 
print '\n'  

print 'Applying amin() function again:' 
print np.amin(a,0) 
print '\n'  

print 'Applying amax() function:' 
print np.amax(a) 
print '\n'  

print 'Applying amax() function again:' 
print np.amax(a, axis = 0)

它将产生以下输出：

Our array is:
[[3 7 5]
[8 4 3]
[2 4 9]]

Applying amin() function:
[3 3 2]

Applying amin() function again:
[2 4 3]

Applying amax() function:
9

Applying amax() function again:
[8 7 9]

numpy.ptp()

numpy.ptp() 函数返回沿轴的值的范围（最大值-最小值）。

import numpy as np 
a = np.array([[3,7,5],[8,4,3],[2,4,9]]) 

print 'Our array is:' 
print a 
print '\n'  

print 'Applying ptp() function:' 
print np.ptp(a) 
print '\n'  

print 'Applying ptp() function along axis 1:' 
print np.ptp(a, axis = 1) 
print '\n'   

print 'Applying ptp() function along axis 0:'
print np.ptp(a, axis = 0) 

它将产生以下输出：

Our array is:
[[3 7 5]
[8 4 3]
[2 4 9]]

Applying ptp() function:
7

Applying ptp() function along axis 1:
[4 5 7]

Applying ptp() function along axis 0:
[6 3 6]

numpy.percentile()

百分位数（或百分位数）是统计学中使用的一种度量，表示一组观测值中低于给定百分比的观测值的数值。numpy.percentile() 函数接受以下参数。

numpy.percentile(a, q, axis)

其中，

示例

import numpy as np 
a = np.array([[30,40,70],[80,20,10],[50,90,60]]) 

print 'Our array is:' 
print a 
print '\n'  

print 'Applying percentile() function:' 
print np.percentile(a,50) 
print '\n'  

print 'Applying percentile() function along axis 1:' 
print np.percentile(a,50, axis = 1) 
print '\n'  

print 'Applying percentile() function along axis 0:' 
print np.percentile(a,50, axis = 0)

它将产生以下输出：

Our array is:
[[30 40 70]
 [80 20 10]
 [50 90 60]]

Applying percentile() function:
50.0

Applying percentile() function along axis 1:
[ 40. 20. 60.]

Applying percentile() function along axis 0:
[ 50. 40. 60.]

numpy.median()

中位数定义为将数据样本的上半部分与下半部分分隔的值。numpy.median() 函数的使用方式如下面的程序所示。

示例

import numpy as np 
a = np.array([[30,65,70],[80,95,10],[50,90,60]]) 

print 'Our array is:' 
print a 
print '\n'  

print 'Applying median() function:' 
print np.median(a) 
print '\n'  

print 'Applying median() function along axis 0:' 
print np.median(a, axis = 0) 
print '\n'  
 
print 'Applying median() function along axis 1:' 
print np.median(a, axis = 1)

它将产生以下输出：

Our array is:
[[30 65 70]
 [80 95 10]
 [50 90 60]]

Applying median() function:
65.0

Applying median() function along axis 0:
[ 50. 90. 60.]

Applying median() function along axis 1:
[ 65. 80. 60.]

numpy.mean()

算术平均值是沿轴的元素之和除以元素的数量。numpy.mean() 函数返回数组中元素的算术平均值。如果指定了轴，则沿该轴计算。

示例

import numpy as np 
a = np.array([[1,2,3],[3,4,5],[4,5,6]]) 

print 'Our array is:' 
print a 
print '\n'  

print 'Applying mean() function:' 
print np.mean(a) 
print '\n'  

print 'Applying mean() function along axis 0:' 
print np.mean(a, axis = 0) 
print '\n'  

print 'Applying mean() function along axis 1:' 
print np.mean(a, axis = 1)

它将产生以下输出：

Our array is:
[[1 2 3]
 [3 4 5]
 [4 5 6]]

Applying mean() function:
3.66666666667

Applying mean() function along axis 0:
[ 2.66666667 3.66666667 4.66666667]

Applying mean() function along axis 1:
[ 2. 4. 5.]

numpy.average()

加权平均值是由每个分量乘以反映其重要性的因子得到的平均值。numpy.average() 函数根据另一个数组中给出的相应权重计算数组中元素的加权平均值。该函数可以具有轴参数。如果未指定轴，则数组将被展平。

考虑一个数组 [1,2,3,4] 和相应的权重 [4,3,2,1]，加权平均值是通过将对应元素的乘积相加并将其和除以权重之和来计算的。

加权平均值 = (1*4+2*3+3*2+4*1)/(4+3+2+1)

示例

import numpy as np 
a = np.array([1,2,3,4]) 

print 'Our array is:' 
print a 
print '\n'  

print 'Applying average() function:' 
print np.average(a) 
print '\n'  

# this is same as mean when weight is not specified 
wts = np.array([4,3,2,1]) 

print 'Applying average() function again:' 
print np.average(a,weights = wts) 
print '\n'  

# Returns the sum of weights, if the returned parameter is set to True. 
print 'Sum of weights' 
print np.average([1,2,3, 4],weights = [4,3,2,1], returned = True)

它将产生以下输出：

Our array is:
[1 2 3 4]

Applying average() function:
2.5

Applying average() function again:
2.0

Sum of weights
(2.0, 10.0)

在多维数组中，可以指定计算的轴。

示例

import numpy as np 
a = np.arange(6).reshape(3,2) 

print 'Our array is:' 
print a 
print '\n'  

print 'Modified array:' 
wt = np.array([3,5]) 
print np.average(a, axis = 1, weights = wt) 
print '\n'  

print 'Modified array:' 
print np.average(a, axis = 1, weights = wt, returned = True)

它将产生以下输出：

Our array is:
[[0 1]
 [2 3]
 [4 5]]

Modified array:
[ 0.625 2.625 4.625]

Modified array:
(array([ 0.625, 2.625, 4.625]), array([ 8., 8., 8.]))

标准差

标准差是平均值的平方偏差的平均值的平方根。标准差的公式如下：

std = sqrt(mean(abs(x - x.mean())**2))

如果数组是 [1, 2, 3, 4]，则其平均值为 2.5。因此，平方偏差为 [2.25, 0.25, 0.25, 2.25]，其平均值的平方根除以 4，即 sqrt (5/4) 为 1.1180339887498949。

示例

import numpy as np 
print np.std([1,2,3,4])

它将产生以下输出：

1.1180339887498949 

方差

方差是平方偏差的平均值，即 mean(abs(x - x.mean())**2)。换句话说，标准差是方差的平方根。

示例

import numpy as np 
print np.var([1,2,3,4])

它将产生以下输出：

1.25