How to segment a gaussian function to equal-volume parts

Question

I'm trying to split a gaussian shaped curve, to K equal-volume segments, with Python for signal-filtering purposes.

I'm seeking for pseudo-code, general idea or a library that performs it. Any help will be much appreciated.

Thanks!

For example in the image below: for K=6. volumes s1 = s2 = ... = s6:

Answer 1

You need to determine percentiles of the distribution. You can use for this scipy.stats.norm class and its .ppf() method.

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

mu = 25
sigma = 4
splits = 8

# define the normal distribution and PDF
dist = sps.norm(loc=mu, scale=sigma)
x = np.linspace(dist.ppf(.001), dist.ppf(.999))
y = dist.pdf(x)

# calculate PPFs
step = 1 / splits
quantiles = np.arange(step, 1.0 - step / 2, step)
ppfs = dist.ppf(quantiles)  # boundaries

# plot results
fig, ax = plt.subplots(figsize=(10, 4))
ax.plot(x, y, color='k')
for i, ppf in enumerate(ppfs):
    ax.axvline(ppf, color=f'C{i}', label=f'{quantiles[i]:.3f}: {ppf:.1f}')
ax.legend()
plt.show()

This is based on this answer