The Kernel

It is advantageous to employ a probability density function (pdf) as the kernel, since then the estimated density is guaranteed to also be a pdf. A common choice of kernel is the Normal pdf, however there is some advantage in using other functions, both those with a higher probability associated with the tail, and those whose contribution to the estimate decreases to zero for points sufficiently remote from the contributor thus allowing the use of a kernel that allows a better fit to the data. For example, in the case of estimating a density that arrives from survival data, there is a distinct advantage in using a kernel with .