Smoothness

Statistics

Mathematical analysis

Multivariate statistics

Density estimation

Artificial intelligence

Variable kernel density estimation

Multivariate kernel density estimation

Probability density function

Kernel (algebra)

Kernel embedding of distributions

Pattern recognition (psychology)

Mathematics

Image (mathematics)

Estimator

Kernel density estimation

Computer science

Bivariate analysis

Support vector machine

Histogram

Discrete mathematics

Kernel method

Univariate

Applied mathematics

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