Compute a confidence interval from sample data assuming unknown distribution

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If you don’t know the underlying distribution, then my first thought would be to use bootstrapping: https://en.wikipedia.org/wiki/Bootstrapping_(statistics)

In pseudo-code, assuming x is a numpy array containing your data:

import numpy as np
N = 10000
mean_estimates = []
for _ in range(N):
    re_sample_idx = np.random.randint(0, len(x), x.shape)
    mean_estimates.append(np.mean(x[re_sample_idx]))

mean_estimates is now a list of 10000 estimates of the mean of the distribution. Take the 2.5th and 97.5th percentile of these 10000 values, and you have a confidence interval around the mean of your data:

sorted_estimates = np.sort(np.array(mean_estimates))
conf_interval = [sorted_estimates[int(0.025 * N)], sorted_estimates[int(0.975 * N)]]

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