[Solved] Probability Distribution Function Python

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This is a minimal working example for showing a histogram. It only solves part of your question, but it can be a step towards your goal. Note that the histogram function gives you the values at the two corners of the bin and you have to interpolate to get the center value.

import numpy as np
import matplotlib.pyplot as pl

x = np.random.randn(10000)

nbins = 20

n, bins = np.histogram(x, nbins, density=1)
pdfx = np.zeros(n.size)
pdfy = np.zeros(n.size)
for k in range(n.size):
    pdfx[k] = 0.5*(bins[k]+bins[k+1])
    pdfy[k] = n[k]

pl.plot(pdfx, pdfy)

You can fit your data using the example shown in:

Fitting empirical distribution to theoretical ones with Scipy (Python)?

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solved Probability Distribution Function Python