Kernel density estimation and its application

Cracow University of Technology, Institute of Water Management and Water Engineering, Warszawska 24, 31-115 Kraków, Poland

^* Corresponding author: sweglar@pk.edu.pl

Abstract

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.