integrable function K. For most applications, it is desirable to define the function to satisfy two additional requirements: Normalization: Symmetry: The first requirement ensures that the method of kernel density estimation results in a probability density function. The second requirement ensures that the average of the corresponding distribution is equal to that of the sample used. If K is a kernel, then so is the function K* defined by K*(u) = λK(λu), where λ > 0. This can be used to select a scale that is appropriate for the data. Kernel functions in common use Several types of kernel functions are commonly used: uniform, triangle, Epanechnikov, quartic (biweight), tricube, triweight, Gaussian, quadratic and cosine. In the table below, if is given with a bounded support, then for values of u lying outside the support. See also Kernel density estimation Kernel smoother Stochastic kernel Positive-definite kernel Density estimation Multivariate kernel density estimation References Nonparametric statistics Time series Point processes Bayesian statistics