python - 总值(value)错误的分布图

Question

创建我用下面的代码制作了分布图:

from numpy import *
import numpy as np
import matplotlib.pyplot as plt

sigma = 4.1

x = np.linspace(-6*sigma, 6*sigma, 200)

def distr(n):
    def g(x):
        return (1/(sigma*sqrt(2*pi)))*exp(-0.5*(x/sigma)**2)
    FxSum = 0
    a = list()
    for i in range(n):
        # divide into 200 parts and sum one by one
        numb = g(-6*sigma + (12*sigma*i)/n)
        FxSum += numb
        a.append(FxSum)
    return a

plt.plot(x, distr(len(x)))
plt.show()

当然，这是一种无需使用 hist()、cdf() 或 Python 库中的任何其他选项即可获取结果的方法。

为什么总和不是1？它不应该依赖于(例如)西格玛。

Answer 1

几乎正确，但为了积分，您必须将函数值 g(x) 乘以微小间隔 dx (12*sigma/200 )。这就是您总结的区域:

from numpy import *
import numpy as np
import matplotlib.pyplot as plt

sigma = 4.1

x = np.linspace(-6*sigma, 6*sigma, 200)

def distr(n):
    def g(x):
        return (1/(sigma*sqrt(2*pi)))*exp(-0.5*(x/sigma)**2)
    FxSum = 0
    a = list()
    for i in range(n):
        # divide into 200 parts and sum one by one
        numb = g(-6*sigma + (12*sigma*i)/n) * (12*sigma/200)
        FxSum += numb
        a.append(FxSum)
    return a

plt.plot(x, distr(len(x)))
plt.show()