如何在Python中绘制这个边界无穷的积分函数?

我在画Marcum函数,它是高斯函数在边界上的积分。

这是函数:

<a href="https://www.codecogs.com/eqnedit.php?latex=Q(y)=\int_{y}^{\infty}\frac{1}{2\pi}\exp(-\frac{x^2}{2})~dx" target="_blank"><img src="https://latex.codecogs.com/gif.latex?Q(y)=\int_{y}^{\infty}\frac{1}{2\pi}\exp(-\frac{x^2}{2})~dx" title="Q(y)=\int_{y}^{\infty}\frac{1}{2\pi}\exp(-\frac{x^2}{2})~dx" /></a>

y是用户必须输入的浮点值。我编写了代码来计算这个函数的期望值。不过,我要画的是这样的:

! https://ibb.co/SRMsfY3

下面是计算Q(y)值的代码:

from scipy.integrate import quad
import scipy, numpy, math
from scipy import integrate


def integrand(x):
   Q_y = (1/(math.sqrt(2*math.pi)))*math.exp((-x**2)/2)
   return Q_y


y = input('y=')
ans, err = quad(integrand, float(y), math.inf)
print(ans)

我试着用下面的代码绘制它:

x_data=np.arange(-20,20,0.1)    
z_data=np.arange(float(y),1000,1)

    ans, err = quad(integrand, float(y), math.inf)
    print(ans)

    for item in x_data:
        z_data[i]=integrand(x_data[i])[0]
        i+=1

    fig = plt.figure(1, figsize=(4,4))
    plt.plot(x_data,z_data,color= 'blue',linestyle='--', label=label1)

返回以下错误:

 File "C:/Users/m.rafiee/.spyder-py3/temp.py", line 59, in <module>
    z_data[i]=integrand(x_data[i])[0]

IndexError: index 400 is out of bounds for axis 0 with size 400

我也不知道如何在绘图中添加如图所示的注释和散列区域。

我非常感谢你事先的帮助。

from scipy.integrate import quad import scipy as sc, numpy as np, math from scipy import integrate import matplotlib.pyplot as plt def integrand(x): Q_y = (1/(math.sqrt(2*math.pi)))*math.exp((-x**2)/2) return Q_y func = np.vectorize(integrand) x = np.arange(-3, 3, 0.1) fig = plt.figure() ax = plt.gca() y = input('y=') y = float(y) result = integrand(y) x_user = np.arange(y, 3, 0.1) ax.axvline(y, color='green', lw=2, alpha=0.5) ax.fill_between(x_user, func(x_user), facecolor="none", hatch="/", edgecolor="red") ax.annotate('Q({0})={1}'.format(y, round(result, 2)), xy=(0, result), xytext=(0, result)) ax.plot(x, func(x))