Fitting normal distribution to weighted histogram in Python

Question

I have a weighted histogram generated by

import numpy as np
import matplotlib.pyplot as plt

data = np.loadtxt('count_rate_data.txt')
hist_bin = [118,121,124,127,130,133,136,139,142,145,148,151,154,157,160,163,166,169,172,175,178,181,184,187,189]
weights=np.ones_like(data)/float(len(data))

plt.hist(data, hist_bin, weights=weights)
plt.grid()

plt.show()

I would like to fit a normal distribution that is weighted to the same extent. How do I do that? I know how to fit a normal distribution to an unweighted histogram. But I am unsure how to fit a normal histogram to a weighted histogram.

So how would you fit the unweighted histogram? (curve fitting, calculating mean and variance, taking the moments, etc.) I guess it will depend on that how to fit the weighted one. — ImportanceOfBeingErnest, Mar 12 '18 at 15:04
From the comments below the answer to that question one sees that it will depend on the purpose of the fit. So without clarification on that this is also too broad. — ImportanceOfBeingErnest, Mar 12 '18 at 15:13

adr · Answer 1 · 2019-10-07T22:11:09.437

The following steps worked for me.

Get the weighted sums:

sums, bins = np.histogram(data, hist_bin, weights=weights)

Make a continuous distribution out of it:

hist_dist = scipy.stats.rv_histogram((sums, bins))

Create a random sample from this distribution:
```
weighted_data = hist_dist.rvs(size=100000)
```
And fit another distribution of your choice, such as the normal one:
```
mean, stdev = scipy.stats.norm.fit(weighted_data)    
```

Fitting normal distribution to weighted histogram in Python

1 Answers1