Thursday, August 16, 2012

Kernel Density Estimation with scipy

This post continues the last one where we have seen how to how to fit two types of distribution functions (Normal and Rayleigh). This time we will see how to use Kernel Density Estimation (KDE) to estimate the probability density function. KDE is a non-parametric technique for density estimation in which a known density function (the kernel) is averaged across the observed data points to create a smooth approximation. Given the non-parametrica nature of KDE, the main estimator has not a fixed functional form but only it depends upon all the data points we used for the estimation. Let's see the snippet:
from scipy.stats.kde import gaussian_kde
from scipy.stats import norm
from numpy import linspace,hstack
from pylab import plot,show,hist

# creating data with two peaks
sampD1 = norm.rvs(loc=-1.0,scale=1,size=300)
sampD2 = norm.rvs(loc=2.0,scale=0.5,size=300)
samp = hstack([sampD1,sampD2])

# obtaining the pdf (my_pdf is a function!)
my_pdf = gaussian_kde(samp)

# plotting the result
x = linspace(-5,5,100)
plot(x,my_pdf(x),'r') # distribution function
hist(samp,normed=1,alpha=.3) # histogram
The result should be as follows: