1、背景想要探究movielens 1M评分数据的评分分布情况是否符合某种分布，做如下假设

2、理论推导

3、算法实现

3.1 数据准备工作

#导入所需要的库
import pandas as pd
import numpy as np
import math
import matplotlib.pyplot as plt

#数据的准备工作
with open("ratings.dat") as file:
    data = []
    for line in file:
        if len(line) != 0:
            data.append(int(line.split(",")[2]))

rating 原始数据VS 单列的评分特征

# 计算theta值
def calTheta(data):
    sum = 0
    for num in data:
        sum += math.log(num,math.e)
    return sum/(len(data))

# 计算sigma值
def calSigma(data,theta):
    sum = 0
    for num in data:
        mid = math.log(num,math.e) - theta
        mid *= mid
        sum += mid
    return math.sqrt(sum/(len(data)))

# 画出图像
def drawP1(sigma,theta):
    x = np.linspace(1,5,5000)
    y = np.array([1/(sigma*i*math.sqrt(2*math.pi))*math.exp(-math.pow(math.log(i,math.e)-theta,2)/(2*sigma*sigma)) for i in x])
    maxNum = y.max()*1.2
    minNum = 0
    plt.plot(x,y)
    plt.ylim(minNum,maxNum)
    plt.show()
    print("sigma is {} theta is {}".format(sigma,theta))

# 主函数
if __name__ == '__main__':
    npdata = np.array(data)
    theta = calTheta(data)
    sigma = calSigma(data,theta)
    drawP1(sigma,theta)

运行结果为：

假设二验证：

# 计算theta值
def calTheta(data):
    sum = 0
    for num in data:
        sum += num
    return sum/(len(data))

# 计算sigma值
def calSigma(data,theta):
    sum = 0
    for num in data:
        mid = num - theta
        mid *= mid
        sum += mid
    return math.sqrt(sum/(len(data)))

# 画出图像
def drawP1(sigma,theta):
    x = np.linspace(-10,10,5000)
    y = np.array([1/(sigma*math.sqrt(2*math.pi))*math.exp(-math.pow(i-theta,2)/(2*sigma*sigma)) for i in x])
    maxNum = y.max()*1.2
    minNum = 0
    plt.plot(x,y)
    plt.ylim(minNum,maxNum)
    plt.show()
# 主函数
if __name__ == '__main__':
#    data = readFile(path)
    npdata = np.array(data)
    theta = calTheta(data)
    sigma = calSigma(data,theta)
    drawP1(sigma,theta)

运行结果：