无法在 python pandas/scipy 中重现偏度测量的结果答案

【问题标题】：Not able to reproduce the result of skewness measure in python pandas/scipy无法在 python pandas/scipy 中重现偏度测量的结果
【发布时间】：2020-12-11 13:19:25
【问题描述】：

我正在尝试从头开始编写偏度度量计算表格。但无法匹配来自 pandas 属性/scipy.stats 函数的值。

我已经浏览了 scipy.stats here 的源代码。但我无法找到我遗漏了什么。

from math import sqrt
from scipy import stats
import pandas as pd
  
def mean(values):
    return sum(values) / len(values)

def standard_dev(values): 
    vals_mean = mean(values)
    numerator = 0
    for val in values:
        numerator += (val - vals_mean) ** 2 
    return sqrt(numerator/len(values))

def skewness(values): 
    n = len(values)
    vals_mean = mean(values)
    thrid_moment = 0
    for val in values: 
        thrid_moment += (val - vals_mean)**3
    return (sqrt(n*(n-1))/ (n-2)) * (thrid_moment / standard_dev(values) ** 3)
  
values = [1,1,1,2,2,3,3,3,4,4,5] 
  
print(f'mean{mean(values)}')
# mean2.6363636363636362

print(f'standard_dev{standard_dev(values)}')
# standard_dev1.2984415324623364

print(f'skewness{skewness(values)}') 
# skewness2.5341000098031734

a = pd.Series(values)
a.std(ddof=0)
# 1.2984415324623364
a.skew()
# 0.23037272816392504

stats.skew(a, bias=False)
# 0.230372728163925
stats.skew(a, bias=True)
# 0.19768660009807223

【问题讨论】：

标签： python pandas scipy statistics

【解决方案1】：

我发现了错误。我没有规范化第三矩值，即没有除以len(values)。

这是完整版：

from math import sqrt 
  
def mean(values):
    return sum(values) / len(values)

def moments(values, moment):
    vals_mean = mean(values)
    numerator = 0
    for val in values:
        numerator += (val - vals_mean) ** moment 
    return numerator/len(values)

def skewness(values): 
    n = len(values)
    m2 = moments(values, 2)
    m3 = moments(values, 3)
    return (sqrt(n*(n-1))/ (n-2)) * (m3 / m2 ** 1.5)
  
values = [1,1,1,2,2, 3,3,3, 4,4, 5] 
  
print(f'mean: {mean(values)}')
print(f'skewness: {skewness(values)}') 
# mean: 2.6363636363636362
# skewness: 0.23037272816392482

【讨论】：