在不进行标准化的情况下，在直方图上精确绘制密度曲线

Question

我需要以直方图的实际高度（实际频率）为y轴在直方图上绘制密度曲线。

Try1： 我找到了一个相关的答案here，但它已将直方图归一化为曲线的范围。

下面是我的代码和输出。

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

data = [125.36, 126.66, 130.28, 133.74, 126.92, 120.85, 119.42, 128.61, 123.53, 130.15, 126.02, 116.65, 125.24, 126.84,
        125.95, 114.41, 138.62, 127.4, 127.59, 123.57, 133.76, 124.6, 113.48, 128.6, 121.04, 119.42, 120.83, 136.53, 120.4,
        136.58, 121.73, 132.72, 109.25, 125.42, 117.67, 124.01, 118.74, 128.99, 131.11, 112.27, 118.76, 119.15, 122.42,
        122.22, 134.71, 126.22, 130.33, 120.52, 126.88, 117.4]
(mu, sigma) = norm.fit(data)
x = np.linspace(min(data), max(data), 100)

plt.hist(data, bins=12, normed=True)
plt.plot(x, mlab.normpdf(x, mu, sigma))

plt.show()

Try2： There @DavidG提供了一个选项，用户定义的功能，即使它不能准确地覆盖直方图的密度。

def gauss_function(x, a, x0, sigma):
    return a * np.exp(-(x - x0) ** 2 / (2 * sigma ** 2))
test = gauss_function(x, max(data), mu, sigma)

plt.hist(data, bins=12)
plt.plot(x, test)
plt.show() 

结果是， 但是实际的直方图如下所示，其中Y轴的范围是0到8， 我想精确地绘制密度曲线。此方面的任何帮助将不胜感激。

Answer 1

这是您要找的吗？我将pdf乘以直方图的面积。

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

data = [125.36, 126.66, 130.28, 133.74, 126.92, 120.85, 119.42, 128.61, 123.53, 130.15, 126.02, 116.65, 125.24, 126.84,
        125.95, 114.41, 138.62, 127.4, 127.59, 123.57, 133.76, 124.6, 113.48, 128.6, 121.04, 119.42, 120.83, 136.53, 120.4,
        136.58, 121.73, 132.72, 109.25, 125.42, 117.67, 124.01, 118.74, 128.99, 131.11, 112.27, 118.76, 119.15, 122.42,
        122.22, 134.71, 126.22, 130.33, 120.52, 126.88, 117.4]

(mu, sigma) = norm.fit(data)
x = np.linspace(min(data), max(data), 100)

values, bins, _ = plt.hist(data, bins=12)
area = sum(np.diff(bins) * values)

plt.plot(x, norm.pdf(x, mu, sigma) * area, 'r')
plt.show()

结果：