python - Scipy正常的pdf评估给出了矛盾的值

Question

我试图写下一个图，表明无偏估计量并不总是最好的估计量。这是我为获得漂亮的图片而编写的代码:

# Set up the plot
fig, ax = plt.subplots()
# Create some data
y = np.linspace(-10, 10, 1000)
# Plot two normals, one centered around 0 but with large variance
ax.plot(y, norm.pdf(y, scale=3), 'k-', label=r"pdf of $\hat{\theta_1}$")
# One centered around 1 with small variance
ax.plot(y, norm.pdf(y, loc=1, scale=1), 'r--', label=r"pdf of $\hat{\theta_2}$")
ax.legend()
# Remove left, right and top axis, remove y axis labels and ticks
ax.spines['left'].set_visible(False)
ax.spines['right'].set_visible(False)
ax.spines['top'].set_visible(False)
ax.tick_params(axis='y', which='both', left=False, right=False, labelleft=False)
# Remove x axis ticks and labels, keep only one at x=0
ax.set_xticks([0])
ax.set_xticklabels([r"$\theta$"])
# Plot vertical line at x=0 from y=0 to the value of the first pdf
ax.axvline(x=0, ymin=0, ymax=norm.pdf(0, scale=3), linestyle=":")
# Plot second vertical line for second normal distribution
ax.axvline(x=1, ymin=0, ymax=norm.pdf(1, loc=1, scale=1), linestyle=":")
# Remove margins so that pdfs lie on the axis
ax.margins(0)
plt.show(block=True)

基本上我想绘制两个正态分布，一个以 0 为中心但方差较大，另一个以 1 为中心且方差较小。然后我想添加两条垂直线。一条线经过 x=0 并在 x=0 处达到第一正态分布的值，第二条线经过 x=1 并在 x=1 处达到第二正态分布的值。然而，这些线要小得多，我不知道为什么!

我唯一的猜测是，由于这些是连续的 pdf，如果我在某个时刻评估它们，scipy 会做一些奇怪的事情。

导入

我忘了提及我的导入，我将它们包含在这里，以便您可以拥有 MWE

import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from scipy.stats import norm

Answer 1

查看 axvline 的文档:

ymax : scalar, optional, default: 1
 Should be between 0 and 1, 0 being the bottom of the plot, 1 the top of the plot.

您的线条是在数据坐标中定义的，而不是在轴坐标中定义的。您需要使用vlines相反。

# Plot vertical line at x=0 from y=0 to the value of the first pdf
ax.vlines(x=0, ymin=0, ymax=norm.pdf(0, scale=3), linestyle=":")
# Plot second vertical line for second normal distribution
ax.vlines(x=1, ymin=0, ymax=norm.pdf(1, loc=1, scale=1), linestyle=":")