Editing Density estimation (section)

== Application and purpose ==
A very natural use of density estimates is in the informal investigation of the properties of a given set of data. 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.<ref>{{Cite book|title=Density Estimation for Statistics and Data Analysis|last=Silverman|first=B. W.|publisher=Chapman and Hall.|year=1986|isbn=978-0412246203|url=https://archive.org/details/densityestimatio00silv_0}}</ref>

[[File:Gumbel distribtion.png|thumb|300px|Histogram and density function for a Gumbel distribution <ref>[https://www.waterlog.info/cumfreq.htm A calculator for probability distributions and density functions]</ref>]]

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.<ref>Geof H., Givens (2013). Computational Statistics. Wiley. p. 330. {{ISBN|978-0-470-53331-4}}.</ref>

Density estimation is also frequently used in [[anomaly detection]] or [[novelty detection]]:<ref>{{cite journal|last1=Pimentel|first1=Marco A.F.|last2=Clifton|first2=David A.|last3=Clifton|first3=Lei|last4=Tarassenko|first4=Lionel|title=A review of novelty detection|journal=Signal Processing|date=2 January 2014|volume= 99|issue=June 2014|pages=215–249|doi=10.1016/j.sigpro.2013.12.026}}</ref> if an observation lies in a very low-density region, it is likely to be an anomaly or a novelty.

* In [[hydrology]] the [[histogram]] and estimated density function of rainfall and river discharge data, analysed with a [[probability distribution]], are used to gain insight in their behaviour and frequency of occurrence.<ref>[https://www.waterlog.info/density.htm An illustration of histograms and probability density functions]</ref> An example is shown in the blue figure.