NumPy 统计函数

NumPy有很多有用的统计函数，用于从给定数组的元素中找到最小值、最大值、百分位数、标准差和方差等。以下是这些函数的解释：

numpy.amin()和numpy.amax()

这些函数返回给定数组中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）是统计学中一个用来指示在一组观察值中，有多少百分比观察值落在某个值以下的度量标准。函数 numpy.percentile() 接受以下参数。

numpy.percentile(a, q, axis)

在这里，

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 被定义为将数据样本的上半部分和下半部分分开的值。 numpy.median() 函数的使用方法如下所示。

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()

算术平均数是沿着一个轴的元素的总和除以元素的数量。 numpy.mean()函数返回数组中元素的算术平均数。如果提及了轴，则沿着该轴计算。

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()

加权平均值是通过将每个分量乘以反映其重要性的因子来计算的平均值。numpy.average()函数根据另一个数组中给定的权重，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，则数组被展平。

假设有一个数组[1,2,3,4]和相应的权重[4,3,2,1]，则加权平均值通过将对应元素的乘积相加，然后除以权重的总和来计算。

加权平均值 = (14+23+32+41)/(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)

它会产生以下输出 –

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

标准差是平均偏差的平方根。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]，那么它的平均值是 2.5。因此，平方偏差是 [2.25，0.25，0.25，2.25]，其平均值的平方根除以 4，即 sqrt (5/4) 是 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

Variance

Variance是平方差的平均值，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