2022年 11月 3日

Python——计算方差、标准差、均方差、均方根值、均方误差、均方根误差

 
  1. # -*- coding: utf-8 -*-
  2.  
  3. import math
  4.  
  5.  
  6. def get_average(records):
  7.     """
  8.     平均值
  9.     """
  10.     return sum(records) / len(records)
  11.  
  12.  
  13. def get_variance(records):
  14.     """
  15.     方差 反映一个数据集的离散程度
  16.     """
  17.     average = get_average(records)
  18.     return sum([(x - average) ** 2 for x in records]) / len(records)
  19.  
  20.  
  21. def get_standard_deviation(records):
  22.     """
  23.     标准差 == 均方差 反映一个数据集的离散程度
  24.     """
  25.     variance = get_variance(records)
  26.     return math.sqrt(variance)
  27.  
  28.  
  29. def get_rms(records):
  30.     """
  31.     均方根值 反映的是有效值而不是平均值
  32.     """
  33.     return math.sqrt(sum([x ** 2 for x in records]) / len(records))
  34.  
  35.  
  36. def get_mse(records_real, records_predict):
  37.     """
  38.     均方误差 估计值与真值 偏差
  39.     """
  40.     if len(records_real) == len(records_predict):
  41.         return sum([(x - y) ** 2 for x, y in zip(records_real, records_predict)]) / len(records_real)
  42.     else:
  43.         return None
  44.  
  45.  
  46. def get_rmse(records_real, records_predict):
  47.     """
  48.     均方根误差：是均方误差的算术平方根
  49.     """
  50.     mse = get_mse(records_real, records_predict)
  51.     if mse:
  52.         return math.sqrt(mse)
  53.     else:
  54.         return None
  55.  
  56.  
  57. def get_mae(records_real, records_predict):
  58.     """
  59.     平均绝对误差
  60.     """
  61.     if len(records_real) == len(records_predict):
  62.         return sum([abs(x - y) for x, y in zip(records_real, records_predict)]) / len(records_real)
  63.     else:
  64.         return None
  65.  
  66.  
  67. if __name__ == '__main__':
  68.     records1 = [3, 4, 5]
  69.     records2 = [2, 4, 6]
  70.  
  71.     # 平均值
  72.     average1 = get_average(records1)  # 4.0
  73.     average2 = get_average(records2)  # 4.0
  74.  
  75.     # 方差
  76.     variance1 = get_variance(records1)  # 0.66
  77.     variance2 = get_variance(records2)  # 2.66
  78.  
  79.     # 标准差
  80.     std_deviation1 = get_standard_deviation(records1)  # 0.81
  81.     std_deviation2 = get_standard_deviation(records2)  # 1.63
  82.  
  83.     # 均方根
  84.     rms1 = get_rms(records1)  # 4.08
  85.     rms2 = get_rms(records2)  # 4.32
  86.  
  87.     # 均方误差
  88.     mse = get_mse(records1, records2)  # 0.66
  89.  
  90.     # 均方根误差
  91.     rmse = get_rmse(records1, records2)  # 0.81
  92.  
  93.     # 平均绝对误差
  94.     mae = get_mae(records1, records2)  # 0.66
  95.   
  96.    print(mae)

注意事项

1、X** 2 表示 X的平方；

2、别忘了包含  import math