将分布拟合到具有不均匀 bin 的数据 python

Question

I have a set of data in histogram format with uneven bin sizes, which represents the weight of horses at a certain point in their lifetimes when they are switched from grazing to a racing diet. Here is a data sample:

Weight - Headcount

0-600lb: 340,000

600-699lb: 365,000

700-799lb: 494,000

800-899lb: 430,000

900-999lb: 110000

1000-3000lb: 40,000

I know that the majority of the 0-600lb category will be towards the heavier end, and the opposite would be true for the 1000-3000lb category, so I'm looking for a decreasing distribution with a peak around the middle. Additionally, this may be a combination of two distributions, as it's possible male and female horses have their diets switched at different times. Then again, maybe not so if a solution without considering this factor would still be fantastic!

How can I try a series of distributions to see which best fits my data in python?

Answer 1

I would assume that this data would follow a normal distribution, so that is where I would start.

When the bin width is even, you can use the bin center as the x value and the bin height as the y . In your case, since the bins are uneven, you should use the bin integral of the objective function to compare to your data. For example the code below:

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

bins = [0, 600, 700, 800, 900, 1000, 3000]
binc = [ 300, 650, 750, 850, 950, 2000]
weights = [340000, 365000, 494000, 430000, 110000, 40000]


def fGaussianCDF(bins, *params):
    
    N = params[0]
    mu = params[1]
    sigma = params[2]

    binwidth = np.diff(bins)

    return N*(scipy.stats.norm.cdf(bins[1:], mu, sigma) - scipy.stats.norm.cdf(bins[:-1], mu, sigma) )


fig, ax = plt.subplots(1, 1)
ax.plot(binc, weights, "ok")
ax.set_xlabel("Weight (lbs.)", fontsize=16)
ax.set_ylabel("Counts", fontsize=16)


popt, _ = scipy.optimize.curve_fit(fGaussianCDF, bins, weights, p0=[1.8e6, 730, 150])
plt.plot(binc, fGaussianCDF(bins, *popt), "rx")
print(popt)

plt.show()

Which gives the best fit result of a mean value of mu=736 lb and sigma=146 . The results plotted look like:

Which is not a perfect fit, but hopefully is something that you are looking for.