NumPy统计函数


NumPy具有相当多的有用的统计函数,用于从数组中的给定元素中找出最小值,最大值,百分位标准偏差和方差等。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。

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)

它会产生以下输出 -

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()

所述 numpy.ptp() 函数沿轴线返回值的范围(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)

它会产生以下输出 -

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)是统计数据中使用的度量,表示一组观测值中给定百分比的观测值下降的值。函数 numpy.percentile() 采用以下参数。

numpy.percentile(a, q, axis)

哪里,

Sr.No. 参数和说明
1 a
输入数组
2 q
计算的百分位数必须在0-100之间
3 axis
要计算百分位数的轴

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)

它会产生以下输出 -

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高半部分与下半部分分开的值。使用 numpy.median() 函数,如下面的程序所示。

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)

它会产生以下输出 -

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的数量。所述 numpy.mean() 函数返回数组中元素的算术平均值。如果提到该轴,则会沿着它进行计算。

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)

它会产生以下输出 -

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()

加权平均数是由每个组件乘以反映其重要性的因素所产生的平均值。所述 numpy.average() 函数根据在另一个数组给定各自的重量计算数组中的元素的加权平均。该功能可以有一个轴参数。如果没有指定轴,则数组变平。

考虑一个数组[1,2,3,4]和相应的权重[4,3,2,1],加权平均值是通过相加元素的乘积和除以权重之和得出的。

加权平均=(1 4 + 2 3 + 3 2 + 4 1)/(4 + 3 + 2 + 1)

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。

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)

它会产生以下输出 -

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.]))

标准偏差

标准偏差是平均偏差平方的平方根。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,平方偏差为[2.25,0.25,0.25,2.25],平均值除以4即sqrt(5/4)的平方根为1.1180339887498949。

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

它会产生以下输出 -

1.1180339887498949

方差

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

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

它会产生以下输出 -

1.25