拟合对数正态函数来计算数据

Question

我有一组粒度数据，这些数据按大小分箱并按分箱宽度标准化。我想为这些数据拟合一个对数正态分布函数，但我遇到了一些问题。大多数软件（例如scipy.stats.lognormal.fit）都需要原始数据，似乎没有办法对已经分箱的数据进行同样的拟合。

将这些数据拟合到对数正态分布的最佳方法是什么？我制作了一个包含可用数据的 csv 文件：https://drive.google.com/file/d/1wxsJuyu7rv0VQBHAYyreZmQqKiIZ7dz5/view?usp=sharing

Answer 1

我发现最好的方法是使用scipy.optimize.curve_fit。下面是一些示例代码，使用上面的示例数据：

import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
from scipy.optimize import curve_fit

# Define lognormal PDF as function of x, mu, and sigma
def lognorm_fit(x, mu, sigma):
    y = (1/(sigma*x*np.sqrt(2*np.pi))) * np.exp(-1* ((np.log(x) - mu)**2/(2*sigma**2)))
    return y

# Open data
df = pd.read_csv('./data.csv')

# Read data, using the lower bin limit as x
count = df['count']
x = df['lower_bin_limit']
width = df['upper_bin_limit'] - df['lower_bin_limit']

# Divide by bin width and normalize by total count
y = count/width/(count.sum())
plt.plot(x,y)

# Use curve_fit to find the two parameters in lognom_fit function
# Curve fit returns a tuple of (mu, sigma) and the covariance,
# Which isn't needed.
(mu,sigma), _ = curve_fit(lognorm_fit, xdata=x, ydata=y)
print(mu, sigma)

# Generate lognorm PDF using values of mu, sigma
yy = lognorm_fit(x, mu, sigma)

# Plot Results
plt.plot(x,y)
plt.plot(x, yy)
plt.xscale('log')
plt.show()