e kernel density. The whole density for a data set is an integration

nel densities. Suppose there are N data points, for which a subset

oints) is used as the kernels. The kernel densities are denoted by

··, ݂ெ, where M ൑ N. The format of the kernel method for

g a density for a data set is shown below,

ܨൌ¹

ܯ^෍݂

ெ

௠

௠ୀଵ

ൌ¹

ܯ^{ሺ݂ଵ൅݂ଶ൅⋯൅݂ெሻ}

(2.5)

ch kernel density ݂௠ is defined as below,

݂௠ൌ

1

√2ߨߪ^{ଶ݁ିሺ௫ି௨೘ሻమ}

ఙ^మ

(2.6)

e 2.10 shows how the kernel-based density estimation works for

. Each dotted curve represents a kernel density centred at one data

e thick curve represents the estimated whole density, which is

d by integrating all kernel densities.

An illustration of how the kernel-based non-parametric approach works for

mation. The bars stand for the density estimated using the histogram approach.

lines stand for the kernel densities. The solid line stands for the final whole

integrating all the kernel densities.

R function for the kernel-based density estimation approach is

density. Its syntax is shown below, in which the compulsory

vector x,

model=density(x,···)