Fitting Binned Lognormal Data In Python

I have a range of particle size distribution data arranged by percentage volume fraction, like so:; size % 6.68 0.05 9.92 1.15 etc. I need to fit this data to a lognormal di

Solution 1:

I guess one possible workaround is to manually fit a pdf to your bin data, assuming x values are the midpoint of each interval, and y values are the corresponding bin frequency. And then fit a curve based on x and y values using scipy.optimize.curve_fit. I think accuracy of the results will depend the number of bins you have. An example is shown below:

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

def pdf(x, mu, sigma):
    """pdf of lognormal distribution"""

    return (np.exp(-(np.log(x) - mu)**2 / (2 * sigma**2)) / (x * sigma * np.sqrt(2 * np.pi)))

mu, sigma = 3., 1.                              # actual parameter value

data = np.random.lognormal(mu, sigma, size=1000)       # data generation
h = plt.hist(data, bins=30, normed = True)

y = h[0]                                        # frequencies for each bin, this is y value to fit 
xs = h[1]                                       # boundaries for each bin
delta = xs[1] - xs[0]                           # width of bins
x = xs[:-1] + delta /                           # midpoints of bins, this is x value to fit

popt, pcov = curve_fit(pdf, x, y, p0=[1, 1])    # data fitting, popt contains the fitted parameters
print(popt)
# [ 3.13048122  1.01360758]                       fitting results

fig, ax = plt.subplots()
ax.hist(data, bins=30, normed=True, align='mid', label='Histogram')
xr = np.linspace(min(xs), max(xs), 10000)
yr = pdf(xr, mu, sigma)
yf = pdf(xr, *popt)
ax.plot(xr, yr, label="Actual")
ax.plot(xr, yf, linestyle = 'dashed', label="Fitted")
ax.legend()