有没有办法将正态曲线拟合到点？

如何解决有没有办法将正态曲线拟合到点？

作为一个小项目，我制作了一个程序，可以多次掷骰子。每次投掷时，它都会对骰子的结果求和并将其添加到列表中。最后用 matplot 绘制数据。

import random
from collections import Counter
import matplotlib.pyplot as plt

nd = int(input("Insert number of dice: ")) 
nt = int(input("Insert number of throws: "))
print(nd," dice thrown ",nt," times")
print("Generating sums,please hold....")
c = 0
i = 0
sum = 0
sums = []
while nt >= i :
    while nd >= c:
        g = random.randint(1,6)
        sum = sum + g
        c += 1
    sums.append(sum)
    i = i+1
    c=0
    sum = 0
    print("Throw ",i," of ",nt)
sums.sort()
max = max(sums)
min = min(sums)
print("||Maximum result: ",max," ||Minimum result: ",min)

print("Now ordering results")

f = Counter(sums)
y = list(f.values())
x = list(f.keys())
print("Rappresenting results")

plt.plot(x,y)
plt.xlabel("Risultati")
plt.ylabel("Frequenza")
plt.title("Distribuzione delle somme")
plt.grid(True)
plt.tight_layout()
plt.show()

结果图如下所示：

我想知道如何将高斯曲线拟合到点上以使图形更清晰

解决方法

总和的均值和标准差是高斯法线所需的参数。分布的 pdf 的面积为 1。要将其缩放到与直方图相同的大小，需要乘以输入值的数量 (len(sums))。

将代码转换为使用 numpy 数组，一切都会变得更快：

import numpy as np
from collections import Counter
import matplotlib.pyplot as plt
from scipy.stats import norm

nd = 10000  # int(input("Insert number of dice: "))
nt = 10000  # int(input("Insert number of throws: "))
print(nd,"dice thrown",nt,"times")
print("Generating sums,please hold....")
sums = np.zeros(nt,dtype=np.int)
for i in range(nt):
    sums[i] = np.sum(np.random.randint(1,7,nd))
sums.sort()
xmax = sums.max()
xmin = sums.min()
print("||Maximum result: ",xmax," ||Minimum result: ",xmin)

print("Now ordering results")

f = Counter(sums)
y = list(f.values())
x = list(f.keys())
print("Plotting results")

plt.plot(x,y)
mean = sums.mean()
std = sums.std()
xs = np.arange(xmin,xmax + 1)
plt.plot(xs,norm.pdf(xs,mean,std) * len(sums),color='red',alpha=0.7,lw=3)
plt.margins(x=0)
plt.xlim(xmin,xmax)
plt.ylim(ymin=0)
plt.tight_layout()
plt.show()

PS：这里有一些代码添加到问题的代码中，使用numpy仅用于计算均值和标准差。 （请注意，当您使用 sum 作为变量名时，当您尝试使用 Python 的 sum() 函数时会出现错误。因此，强烈建议避免将变量命名为 sum和max。）

def f(x):
    return norm.pdf(x,std) * len(sums)

mean = np.mean(sums)
std = np.std(sums)
xs = range(xmin,xmax+1)
ys = [f(x) for x in xs]
plt.plot(xs,ys,lw=3)