Histograms for Probability Density Estimation: A Primer

[bagrow]

The best way to compute the empirical CDF (ECDF) is by sorting the data:

    N = len(data)
    X = sorted(data)
    Y = np.arange(N)/N
    plt.plot(X,Y)

Technically, you should plot this with `plt.step`.

[andrewla]

scipy even has a built-in method (scipy.stats.ecdf) for doing exactly this.

[sobriquet9]

Why estimate PDF through histogram then convert to CDF, when one can estimate CDF directly? Doing so also avoids having to choose bin width that can have substantial impact.

[andrewla]

Agreed -- very odd to use a parameter (bin width) in a nonparametric estimation. Just use the raw data. In numerical analysis, broadly speaking, integrals are stable while derivatives are wild; an empirical cdf is a nice smooth integral of the messy pdf.

[Bostonian]

If the data is continuous, use kernel density estimation (KDE) instead of histograms to visualize the probability density, since KDE will give a smoother fit. A similar idea is to fit a mixture of normals -- there are numerous R packages for this and sklearn.mixture.GaussianMixture in SciPy.

[vvanirudh]

Yep! The next post would be on Kernel density estimation -- wanted to start from histograms as they are still a useful tool in 1-D and 2-D density estimation, and you don't have to store the data either (unlike KDE)