Density estimation

For the signal processing concept, see spectral density estimation.
Demonstration of density estimation using Kernel density estimation: The true density is a mixture of two Gaussians centered around 0 and 3, shown with a solid blue curve. In each frame, 100 samples are generated from the distribution, shown in red. Centered on each sample, a Gaussian kernel is drawn in gray. Averaging the Gaussians yields the density estimate shown in the dashed black curve.

In statistics, probability density estimation or simply density estimation is the construction of an estimate, based on observed data, of an unobservable underlying probability density function. The unobservable density function is thought of as the density according to which a large population is distributed; the data are usually thought of as a random sample from that population.[1]

A variety of approaches to density estimation are used, including Parzen windows and a range of data clustering techniques, including vector quantization. The most basic form of density estimation is a rescaled histogram.

  1. ^ Alberto Bernacchia, Simone Pigolotti, Self-Consistent Method for Density Estimation, Journal of the Royal Statistical Society Series B: Statistical Methodology, Volume 73, Issue 3, June 2011, Pages 407–422, https://doi.org/10.1111/j.1467-9868.2011.00772.x