使用Scipy绘制skewnorm时曲线幅值异常偏低的问题

问题核心是直方图默认统计量和PDF的量纲不一致：

• 直方图默认展示每个区间的样本频数（数量）
• skewnorm.pdf()输出的是概率密度值，其积分和为1，数值范围远小于频数

只要调整直方图的归一化模式，就能让两者完美匹配，以下是修正后的完整代码：

from scipy import stats
import matplotlib.pyplot as plt
import numpy as np

data = [ 10, 10, 11, 10, 11, 11, 10, 10, 15, 15, 14, 18, 11, 10, 11, 13, 13, 10, 13, 16
       , 16, 15, 11, 16, 12, 11, 17, 13, 11, 14, 12, 11, 10, 12, 11, 12, 10, 12, 10, 12
       , 11, 11, 11, 12, 15, 11, 12, 12, 10, 12, 10, 10, 11, 11, 14, 10, 11, 10, 17, 10
       , 15, 10, 11, 11, 10, 9, 12, 11, 13, 12, 12, 11, 11, 16, 15, 21, 11, 11, 11, 13
       , 11, 12, 10, 21, 10, 13, 10, 10, 13, 13, 10, 18, 13, 13, 11, 14, 10, 14, 13, 11
       , 10, 12, 15, 9, 10, 9, 16, 14, 15, 11, 10, 11, 10, 11, 12, 12, 12, 12, 10, 10
       , 10, 11, 13, 11, 19, 11, 15, 13, 13, 11, 10, 13, 10, 10, 10, 12, 10, 10, 18, 12
       , 12, 13, 11, 17, 10, 11, 10, 14, 12, 12, 14, 10, 15, 10, 10, 12, 12, 11, 10, 25
       , 11, 13, 10, 11, 12, 12, 12, 17, 12, 11, 10, 11, 24, 10, 10, 10, 13, 10, 11, 12
       , 10, 12, 12, 11, 24, 11, 15, 11, 13, 13, 12, 11, 10, 11, 10, 12, 10]

X = np.linspace(min(data), max(data), num=200)

# 拟合偏态正态分布参数并计算PDF值
params = stats.skewnorm.fit(data)
pdf = stats.skewnorm.pdf(X, *params)

fig, ax = plt.subplots()
# 关键改动：添加density=True，将直方图归一化为概率密度
ax.hist(data, bins=25, density=True, alpha=0.6, label='样本直方图')
ax.plot(X, pdf, 'r-', linewidth=2, label='拟合偏态正态分布')

# 优化图表可读性
ax.set_xlabel('数值')
ax.set_ylabel('概率密度')
ax.set_title('样本数据与拟合偏态正态分布对比')
ax.legend()

fig.savefig("test.png")
plt.show()

可选方案：如果要展示频数而非概率密度 #

如果需要保持直方图的频数统计模式，可以通过样本总数乘以区间宽度来缩放PDF曲线：

n, bins, patches = ax.hist(data, bins=25, alpha=0.6, label='样本直方图')
bin_width = bins[1] - bins[0]
# 缩放PDF以匹配频数幅值
ax.plot(X, pdf * len(data) * bin_width, 'r-', linewidth=2, label='拟合偏态正态分布')

内容的提问来源于stack exchange，提问作者Robert