python - Plotting probability density function by sample with matplotlib

Question

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Closed 8 years ago.

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 1

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:

Answer 2

What you have to do is to use the gaussian_kde from the scipy.stats.kde package.

given your data you can do something like this:

from scipy.stats.kde import gaussian_kde
from numpy import linspace
# create fake data
data = randn(1000)
# this create the kernel, given an array it will estimate the probability over that values
kde = gaussian_kde( data )
# these are the values over wich your kernel will be evaluated
dist_space = linspace( min(data), max(data), 100 )
# plot the results
plt.plot( dist_space, kde(dist_space) )

The kernel density can be configured at will and can handle N-dimensional data with ease. It will also avoid the spline distorsion that you can see in the plot given by askewchan.