I am trying to compare a Kernel Density estimation with a normal distribution.
I use the following code to estimate the Kernel Density using a Epanechnikov kernel:
from sklearn.neighbors.kde import KernelDensity X_grid = np.linspace(-5, 5, num=1000) def silverman_bw(ts): return 1.3643*1.7188*len(ts)**(-0.2)*min(np.std(ts), np.subtract(*np.percentile(ts, [75, 25]))) kde = KernelDensity(kernel='epanechnikov', bandwidth=silverman_bw(ts5m.logreturns)).fit(ts5m.logreturns.reshape(-1,1)) pdf = np.exp(kde5m.score_samples(X_grid.reshape(-1,1)))
and the following code to generate the Normal Distribution I want to benchmark it up against
from scipy.stats.distributions import norm normpdf = norm.pdf(X_grid)
The problem is obvious when I plot these two in the same plot; it is impossible to compare the two distributions due to different y-scales. The red line is the Kernel Density estimate and the blue-ish the Normal Distribution.
What do I do in order to be able to compare these two? I am probably missing some scaling/standardization-something, but I just can't remember the precise theory, and I am unable to find answers in my academic litterature.