I want to plot an approximation of probability density function based on a sample that I have; The curve that mimics the histogram behaviour. I can have samples as big as I want.

## Answer

If you want to plot a distribution, and you know it, define it as a function, and plot it as so:

import numpy as np from matplotlib import pyplot as plt def my_dist(x): return np.exp(-x ** 2) x = np.arange(-100, 100) p = my_dist(x) plt.plot(x, p) plt.show()

If you don’t have the exact distribution as an analytical function, perhaps you can generate a large sample, take a histogram and somehow smooth the data:

import numpy as np from scipy.interpolate import UnivariateSpline from matplotlib import pyplot as plt N = 1000 n = N//10 s = np.random.normal(size=N) # generate your data sample with N elements p, x = np.histogram(s, bins=n) # bin it into n = N//10 bins x = x[:-1] + (x[1] - x[0])/2 # convert bin edges to centers f = UnivariateSpline(x, p, s=n) plt.plot(x, f(x)) plt.show()

You can increase or decrease `s`

(smoothing factor) within the `UnivariateSpline`

function call to increase or decrease smoothing. For example, using the two you get: