Density estimation

Density estimates can give a valuable indication of such features as skewness and multimodality in the data.

In some cases they will yield conclusions that may then be regarded as self-evidently true, while in others all they will do is to point the way to further analysis and/or data collection.

[5] An important aspect of statistics is often the presentation of data back to the client in order to provide explanation and illustration of conclusions that may possibly have been obtained by other means.

Density estimates are ideal for this purpose, for the simple reason that they are fairly easily comprehensible to non-mathematicians.

More examples illustrating the use of density estimates for exploratory and presentational purposes, including the important case of bivariate data.

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.
Estimated density of p (glu | diabetes=1) (red), p (glu | diabetes=0) (blue), and p (glu) (black)
Estimated probability of p (diabetes=1 | glu)
Estimated probability of p (diabetes=1 | glu)
Histogram and density function for a Gumbel distribution [ 6 ]
Kernel density estimation of 100 normally distributed random numbers using different smoothing bandwidths.