Histogram

Discrete mathematics

Statistics

Multivariate statistics

Support vector machine

Applied mathematics

Variable kernel density estimation

Computer science

Kernel embedding of distributions

Kernel (algebra)

Pattern recognition (psychology)

Mathematics

Estimator

Image (mathematics)

Kernel density estimation

Kernel method

Smoothness

Mathematical analysis

Artificial intelligence

Multivariate kernel density estimation

Probability density function

Density estimation

Univariate

ITM Web of Conferences

Kernel density estimation is a technique for estimation of probability density function that is a must-have enabling the user to better analyse the studied probability distribution than when using a traditional histogram. Unlike the histogram, the kernel technique produces smooth estimate of the pdf, uses all sample points' locations and more convincingly suggest multimodality. In its two-dimensional applications, kernel estimation is even better as the 2D histogram requires additionally to define the orientation of 2D bins. Two concepts play fundamental role in kernel estimation: kernel function shape and coefficient of smoothness, of which the latter is crucial to the method. Several real-life examples, both for univariate and bivariate applications, are shown.

Kernel density estimation and its application