如何使用我自己的數據在 Python 中應用多元正態 pdf function

Question

我使用以下代碼生成隨機數據和 plot 概率密度分布。 我怎樣才能對我自己的數據做同樣的事情，如下所示？

代碼

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

mean, cov = [0, 1], [(1, .5), (.5, 1)]
data = np.random.multivariate_normal(mean, cov, 200)
df = pd.DataFrame(data, columns=["X", "Y"])
x, y = np.random.multivariate_normal(mean, cov, 1000).T

g = sns.jointplot(x=x, y=y, data=df, kind="kde", n_levels=75, color="m")
g.plot_joint(plt.scatter, c="black", s=30, linewidth=1, marker="+")
g.ax_joint.collections[0].set_alpha(0)
g.set_axis_labels("X", "Y");

我自己的數據樣本

        X       Y
0       1       8
1       7       8
2       7       9
3       5       8
4       7       7
5       9       9
6       1       3
4       6       8
5       9       7
6       9       6
7       8       2
8       1       9
9       0       10
10      22      2
11      4       45
12      9       8

我試過了，但我得到了奇怪的值

import numpy as np

mean = np.mean(data1['X'], axis=0)
cov = np.cov(data1['Y'], rowvar=0)
X = multivariate_normal.pdf(data1['X'], mean=2.5, cov=0.5)

mean = np.mean(data1['X'], axis=0)
cov = np.cov(data1['Y'], rowvar=0)
Y = multivariate_normal.pdf(data1['Y'], mean=2.5, cov=0.5)

df = np.concatenate( (X.reshape(-1,1),Y.reshape(-1,1)) , axis=1)
df = pd.DataFrame(df)
df =  df.rename({0: 'X', 1: 'Y'}, axis=1) 

g = sns.jointplot(x=X, y=Y, data=df, kind="kde", n_levels=75, color="r")
g.plot_joint(plt.scatter, c="black", s=30, linewidth=1, marker="+")
g.ax_joint.collections[0].set_alpha(0)
g.set_axis_labels("X", "Y");

Answer 1

這個解決方案奏效了。

import numpy as np

mean = np.mean(data1['X'], axis=0)
cov = np.cov(data1['Y'], rowvar=0)
X = multivariate_normal.pdf(data1['X'], mean=2.5, cov=0.5)

mean = np.mean(data1['X'], axis=0)
cov = np.cov(data1['Y'], rowvar=0)
Y = multivariate_normal.pdf(data1['Y'], mean=2.5, cov=0.5)

df = np.concatenate( (X.reshape(-1,1),Y.reshape(-1,1)) , axis=1)
df = pd.DataFrame(df)
df =  df.rename({0: 'X', 1: 'Y'}, axis=1) 

g = sns.jointplot(x=X, y=Y, data=df, kind="kde", n_levels=75, color="r")
g.plot_joint(plt.scatter, c="black", s=30, linewidth=1, marker="+")
g.ax_joint.collections[0].set_alpha(0)
g.set_axis_labels("X", "Y");