如何使用python / numpy计算百分位数？

是否有一种方便的方法来计算序列或一维numpy数组的百分位数？

我正在寻找类似于Excel的百分位数功能的东西。

我查看了NumPy的统计资料参考，但找不到。我只能找到中位数（第50个百分位数），但没有更具体的内容。

您可能对SciPy Stats软件包感兴趣。它具有您需要的百分位数功能和许多其他统计功能。

percentile() 可在numpy太。

import numpy as np
a = np.array([1,2,3,4,5])
p = np.percentile(a, 50) # return 50th percentile, e.g median.
print p
3.0

这张票使我相信他们不会percentile()很快集成到numpy中。

顺便说一句，有一个纯Python实现的百分位数功能，以防万一不想依赖scipy。该函数复制如下：

## {{{ http://code.activestate.com/recipes/511478/ (r1)
import math
import functools

def percentile(N, percent, key=lambda x:x):
    """
    Find the percentile of a list of values.

    @parameter N - is a list of values. Note N MUST BE already sorted.
    @parameter percent - a float value from 0.0 to 1.0.
    @parameter key - optional key function to compute value from each element of N.

    @return - the percentile of the values
    """
    if not N:
        return None
    k = (len(N)-1) * percent
    f = math.floor(k)
    c = math.ceil(k)
    if f == c:
        return key(N[int(k)])
    d0 = key(N[int(f)]) * (c-k)
    d1 = key(N[int(c)]) * (k-f)
    return d0+d1

# median is 50th percentile.
median = functools.partial(percentile, percent=0.5)
## end of http://code.activestate.com/recipes/511478/ }}}

import numpy as np
a = [154, 400, 1124, 82, 94, 108]
print np.percentile(a,95) # gives the 95th percentile

这是不使用numpy的方法，仅使用python计算百分位数。

import math

def percentile(data, percentile):
    size = len(data)
    return sorted(data)[int(math.ceil((size * percentile) / 100)) - 1]

p5 = percentile(mylist, 5)
p25 = percentile(mylist, 25)
p50 = percentile(mylist, 50)
p75 = percentile(mylist, 75)
p95 = percentile(mylist, 95)

我通常看到的百分位数定义期望结果是所提供的列表中的值，在该列表下找到P值的百分比...这意味着结果必须来自集合，而不是集合元素之间的插值。为此，您可以使用更简单的功能。

def percentile(N, P):
    """
    Find the percentile of a list of values

    @parameter N - A list of values.  N must be sorted.
    @parameter P - A float value from 0.0 to 1.0

    @return - The percentile of the values.
    """
    n = int(round(P * len(N) + 0.5))
    return N[n-1]

# A = (1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
# B = (15, 20, 35, 40, 50)
#
# print percentile(A, P=0.3)
# 4
# print percentile(A, P=0.8)
# 9
# print percentile(B, P=0.3)
# 20
# print percentile(B, P=0.8)
# 50

如果您希望从提供的列表中获取等于或低于P值百分比的值，请使用以下简单修改：

def percentile(N, P):
    n = int(round(P * len(N) + 0.5))
    if n > 1:
        return N[n-2]
    else:
        return N[0]

或使用@ijustlovemath建议的简化形式：

def percentile(N, P):
    n = max(int(round(P * len(N) + 0.5)), 2)
    return N[n-2]

从开始Python 3.8，标准库附带的quantiles功能作为statistics模块的一部分：

from statistics import quantiles

quantiles([1, 2, 3, 4, 5], n=100)
# [0.06, 0.12, 0.18, 0.24, 0.3, 0.36, 0.42, 0.48, 0.54, 0.6, 0.66, 0.72, 0.78, 0.84, 0.9, 0.96, 1.02, 1.08, 1.14, 1.2, 1.26, 1.32, 1.38, 1.44, 1.5, 1.56, 1.62, 1.68, 1.74, 1.8, 1.86, 1.92, 1.98, 2.04, 2.1, 2.16, 2.22, 2.28, 2.34, 2.4, 2.46, 2.52, 2.58, 2.64, 2.7, 2.76, 2.82, 2.88, 2.94, 3.0, 3.06, 3.12, 3.18, 3.24, 3.3, 3.36, 3.42, 3.48, 3.54, 3.6, 3.66, 3.72, 3.78, 3.84, 3.9, 3.96, 4.02, 4.08, 4.14, 4.2, 4.26, 4.32, 4.38, 4.44, 4.5, 4.56, 4.62, 4.68, 4.74, 4.8, 4.86, 4.92, 4.98, 5.04, 5.1, 5.16, 5.22, 5.28, 5.34, 5.4, 5.46, 5.52, 5.58, 5.64, 5.7, 5.76, 5.82, 5.88, 5.94]
quantiles([1, 2, 3, 4, 5], n=100)[49] # 50th percentile (e.g median)
# 3.0

quantiles对于给定的分布，返回切分点dist列表，这些n - 1切点将分n位数间隔（以等概率dist分为n连续间隔）划分为：

statistics.quantiles（dist，*，n = 4，method ='exclusive'）

在那里n，在我们的案例（percentiles）是100。

检查scipy.stats模块：

 scipy.stats.scoreatpercentile

要计算系列的百分位数，请运行：

from scipy.stats import rankdata
import numpy as np

def calc_percentile(a, method='min'):
    if isinstance(a, list):
        a = np.asarray(a)
    return rankdata(a, method=method) / float(len(a))

例如：

a = range(20)
print {val: round(percentile, 3) for val, percentile in zip(a, calc_percentile(a))}
>>> {0: 0.05, 1: 0.1, 2: 0.15, 3: 0.2, 4: 0.25, 5: 0.3, 6: 0.35, 7: 0.4, 8: 0.45, 9: 0.5, 10: 0.55, 11: 0.6, 12: 0.65, 13: 0.7, 14: 0.75, 15: 0.8, 16: 0.85, 17: 0.9, 18: 0.95, 19: 1.0}

如果您需要答案成为输入numpy数组的成员，请执行以下操作：

只是要补充一点，默认情况下numpy中的percentile函数将输出计算为输入向量中两个相邻条目的线性加权平均值。在某些情况下，人们可能希望返回的百分位数是向量的实际元素，在这种情况下，从v1.9.0开始，您可以使用“插值”选项，并使用“较低”，“较高”或“最近”。

import numpy as np
x=np.random.uniform(10,size=(1000))-5.0

np.percentile(x,70) # 70th percentile

2.075966046220879

np.percentile(x,70,interpolation="nearest")

2.0729677997904314

后者是向量中的实际项，而前者是两个向量项的线性插值，它们与百分位数接壤

适用于一系列：用于描述功能

假设您的df包含以下列sales和id。您想要计算销售百分比，则它的工作原理如下：

df['sales'].describe(percentiles = [0.0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1])

0.0: .0: minimum
1: maximum 
0.1 : 10th percentile and so on

计算一维numpy序列或矩阵的百分位数的便捷方法是使用numpy.percentile < https://docs.scipy.org/doc/numpy/reference/generated/numpy.percentile.html >。例：

import numpy as np

a = np.array([0,1,2,3,4,5,6,7,8,9,10])
p50 = np.percentile(a, 50) # return 50th percentile, e.g median.
p90 = np.percentile(a, 90) # return 90th percentile.
print('median = ',p50,' and p90 = ',p90) # median =  5.0  and p90 =  9.0

但是，如果您的数据中有任何NaN值，则上述功能将无用。在这种情况下，建议使用的函数是numpy.nanpercentile < https://docs.scipy.org/doc/numpy/reference/generation/numpy.nanpercentile.html >函数：

import numpy as np

a_NaN = np.array([0.,1.,2.,3.,4.,5.,6.,7.,8.,9.,10.])
a_NaN[0] = np.nan
print('a_NaN',a_NaN)
p50 = np.nanpercentile(a_NaN, 50) # return 50th percentile, e.g median.
p90 = np.nanpercentile(a_NaN, 90) # return 90th percentile.
print('median = ',p50,' and p90 = ',p90) # median =  5.5  and p90 =  9.1

在上面显示的两个选项中，您仍然可以选择插值模式。请按照以下示例进行操作，以便于理解。

import numpy as np

b = np.array([1,2,3,4,5,6,7,8,9,10])
print('percentiles using default interpolation')
p10 = np.percentile(b, 10) # return 10th percentile.
p50 = np.percentile(b, 50) # return 50th percentile, e.g median.
p90 = np.percentile(b, 90) # return 90th percentile.
print('p10 = ',p10,', median = ',p50,' and p90 = ',p90)
#p10 =  1.9 , median =  5.5  and p90 =  9.1

print('percentiles using interpolation = ', "linear")
p10 = np.percentile(b, 10,interpolation='linear') # return 10th percentile.
p50 = np.percentile(b, 50,interpolation='linear') # return 50th percentile, e.g median.
p90 = np.percentile(b, 90,interpolation='linear') # return 90th percentile.
print('p10 = ',p10,', median = ',p50,' and p90 = ',p90)
#p10 =  1.9 , median =  5.5  and p90 =  9.1

print('percentiles using interpolation = ', "lower")
p10 = np.percentile(b, 10,interpolation='lower') # return 10th percentile.
p50 = np.percentile(b, 50,interpolation='lower') # return 50th percentile, e.g median.
p90 = np.percentile(b, 90,interpolation='lower') # return 90th percentile.
print('p10 = ',p10,', median = ',p50,' and p90 = ',p90)
#p10 =  1 , median =  5  and p90 =  9

print('percentiles using interpolation = ', "higher")
p10 = np.percentile(b, 10,interpolation='higher') # return 10th percentile.
p50 = np.percentile(b, 50,interpolation='higher') # return 50th percentile, e.g median.
p90 = np.percentile(b, 90,interpolation='higher') # return 90th percentile.
print('p10 = ',p10,', median = ',p50,' and p90 = ',p90)
#p10 =  2 , median =  6  and p90 =  10

print('percentiles using interpolation = ', "midpoint")
p10 = np.percentile(b, 10,interpolation='midpoint') # return 10th percentile.
p50 = np.percentile(b, 50,interpolation='midpoint') # return 50th percentile, e.g median.
p90 = np.percentile(b, 90,interpolation='midpoint') # return 90th percentile.
print('p10 = ',p10,', median = ',p50,' and p90 = ',p90)
#p10 =  1.5 , median =  5.5  and p90 =  9.5

print('percentiles using interpolation = ', "nearest")
p10 = np.percentile(b, 10,interpolation='nearest') # return 10th percentile.
p50 = np.percentile(b, 50,interpolation='nearest') # return 50th percentile, e.g median.
p90 = np.percentile(b, 90,interpolation='nearest') # return 90th percentile.
print('p10 = ',p10,', median = ',p50,' and p90 = ',p90)
#p10 =  2 , median =  5  and p90 =  9

如果您的输入数组仅包含整数值，那么您可能会对百分位数答案作为整数感兴趣。如果是这样，请选择插值模式，例如“较低”，“较高”或“最近”。