NumPy - 统计函数

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NumPy 有很多有用的统计函数，用于从数组中的给定元素中查找最小值、最大值、百分位数标准差和方差等。这些功能解释如下 -

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。

例子

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）是统计中使用的一种度量，指示一组观测值中给定百分比的观测值低于该值的值。函数numpy.percentile()采用以下参数。

numpy.percentile(a, q, axis)

在哪里，

例子

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开的值。numpy.median ()函数的用法如以下程序所示。

例子

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总和除以元素数量。numpy.mean ()函数返回数组中元素的算术平均值。如果提到了轴，则沿着它计算。

例子

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() 平均

加权平均值是每个组成部分乘以反映其重要性的因素得出的平均值。numpy.average ()函数根据另一个数组中给定的各自权重计算数组中元素的加权平均值。该函数可以有一个轴参数。如果未指定轴，则数组将被展平。

考虑数组 [1,2,3,4] 和相应的权重 [4,3,2,1]，通过将相应元素的乘积相加并将总和除以权重总和来计算加权平均值。

加权平均值=(1*4+2*3+3*2+4*1)/(4+3+2+1)

例子

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。

例子

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))

如果数组为 [1, 2, 3, 4]，则其平均值为 2.5。因此，偏差平方为 [2.25, 0.25, 0.25, 2.25]，其均值除以 4 的平方根，即 sqrt (5/4) 为 1.1180339887498949。

例子

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

它将产生以下输出 -

1.1180339887498949 

方差

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

例子

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

它将产生以下输出 -

1.25