#!/usr/bin/python3.7
# -*- coding: utf-8 -*-
# @Time : 2019/3/21 14:59
# @Author: Jtyoui@qq.com
from jtyoui.decorators import parameter_set_length
"""
平均值,中位数,众数,分位数,极差,方差,标准差,偏度,峰度
"""
[文档]class AnalysisMath:
def __init__(self, data=()):
if not isinstance(data, (set, list, tuple)):
raise TypeError("传入一个可替代对象.比如list,set,tuple类型")
self.__data = data
self.__length = len(data)
[文档] def average(self, flag=0):
"""平均数
flag=0 算术平均值
flag=1 几何平均值
flag=2 平方平均值(均方根)
flag=3 调和平均值
:param flag: 根据不同的数值,进行不同的平均值
"""
if flag == 0:
return sum(self.__data) / self.__length
elif flag == 1:
all_ = 1
for data in self.__data:
all_ *= abs(data)
return pow(all_, self.__length)
elif flag == 2:
all_ = [data ** 2 for data in self.__data]
return pow(sum(all_) / self.__length, 0.5)
elif flag == 3:
all_ = [1 / data for data in self.__data]
return self.__length / sum(all_)
[文档] def expect(self, data=None):
"""数学期望"""
if data:
self.__init__(data)
return self.average(0)
@property
def median(self):
"""中位数"""
return self.quantile(2)
@property
def mode_number(self):
"""众数"""
data = {}
for d in self.__data:
data[d] = data.get(d, 0) + 1
max_ = sorted(data.items(), key=lambda x: x[1], reverse=True)
return max_[0][0]
[文档] def quantile(self, position=1):
"""分位数
position=1: 第一四分位数 (Q1)，又称“较小四分位数”，等于该样本中所有数值由小到大排列后第25%的数字。
position=2: 第二四分位数 (Q2)，又称“中位数”，等于该样本中所有数值由小到大排列后第50%的数字。
position=3: 第三四分位数 (Q3)，又称“较大四分位数”，等于该样本中所有数值由小到大排列后第75%的数字。
:param position: 根据不同的数值计算不同的分位数
"""
if position > 3:
raise ValueError("position的取值范围是[1,2,3]整数")
data = sorted(self.__data)
middle, mod = divmod(self.__length * position, 4)
if mod == 0:
return (data[middle - 1] + data[middle]) / 2
else:
return data[middle]
@property
def range(self):
"""极差"""
return max(self.__data) - min(self.__data)
[文档] def variance(self, data=None):
"""方差"""
if data:
self.__init__(data)
average = self.average(0)
all_ = [(data - average) ** 2 for data in self.__data]
return sum(all_) / self.__length
[文档] def standard(self, data=None):
"""标准差"""
if data:
self.__init__(data)
return pow(self.variance(), 0.5)
@property
def skewness(self):
"""偏度(偏态系数)"""
x_3 = [data ** 3 for data in self.__data]
x_2 = [data ** 2 for data in self.__data]
expect_1 = self.average(0) # x的数学期望
expect_3 = sum(x_3) / self.__length # x**3的数学期望
expect_2 = sum(x_2) / self.__length # x**2的数学期望
numerator = expect_3 - 3 * expect_1 * (expect_2 - expect_1 ** 2) - expect_1 ** 3 # 分子
denominator = pow(expect_2 - expect_1 ** 2, 1.5) # 分母
return numerator / denominator
@property
def kurtosis(self):
"""峰度
如果超值峰度为正，称为尖峰态
如果超值峰度为负，称为低峰态
"""
average = self.average(0) # 数学期望
all_4 = [(data - average) ** 4 for data in self.__data]
numerator = sum(all_4) / self.__length # 四阶样本中心矩
denominator = self.standard() ** 4 # 标准差**4
return numerator / denominator - 3 # 通常将峰度值做减3处理，使得正态分布的峰度0
[文档]@parameter_set_length
def cov(x, y):
"""协方差
:return: 表示x的数学期望
"""
if isinstance(x, (set, list, tuple)) and isinstance(y, (set, list, tuple)):
ana = AnalysisMath()
expect_x = ana.expect(x)
expect_y = ana.expect(y)
xy = [x_ * y_ for x_, y_ in zip(x, y)]
expect_xy = ana.expect(xy)
return expect_xy - expect_x * expect_y
else:
raise TypeError("x,y类型必须满足其中一个(set, list, tuple)")
if __name__ == '__main__':
analysis = AnalysisMath(data=[1, 2, 3, 5, 7, 2, 4, 2, 8, 9])
print(analysis.average(3))
print(analysis.median)
print(analysis.mode_number)
print(analysis.quantile(2))
print(analysis.range)
print(analysis.variance())
print(analysis.standard())
print(analysis.skewness)
print(analysis.kurtosis)