# bkde {KernSmooth}

### Description

Returns x and y coordinates of the binned kernel density estimate of the probability density of the data.

### Usage

bkde(x, kernel = "normal", canonical = FALSE, bandwidth, gridsize = 401L, range.x, truncate = TRUE)

### Arguments

- x
- numeric vector of observations from the distribution whose density is to be estimated. Missing values are not allowed.
- bandwidth
- the kernel bandwidth smoothing parameter. Larger values of
`bandwidth`

make smoother estimates, smaller values of`bandwidth`

make less smooth estimates. The default is a bandwidth computed from the variance of`x`

, specifically the ‘oversmoothed bandwidth selector’ of Wand and Jones (1995, page 61). - kernel
- character string which determines the smoothing kernel.
`kernel`

can be:`"normal"`

- the Gaussian density function (the default).`"box"`

- a rectangular box.`"epanech"`

- the centred beta(2,2) density.`"biweight"`

- the centred beta(3,3) density.`"triweight"`

- the centred beta(4,4) density. This can be abbreviated to any unique abbreviation. - canonical
- logical flag: if
`TRUE`

, canonically scaled kernels are used. - gridsize
- the number of equally spaced points at which to estimate the density.
- range.x
- vector containing the minimum and maximum values of
`x`

at which to compute the estimate. The default is the minimum and maximum data values, extended by the support of the kernel. - truncate
- logical flag: if
`TRUE`

, data with`x`

values outside the range specified by`range.x`

are ignored.

### Details

This is the binned approximation to the ordinary kernel density estimate. Linear binning is used to obtain the bin counts. For each `x`

value in the sample, the kernel is centered on that `x`

and the heights of the kernel at each datapoint are summed. This sum, after a normalization, is the corresponding `y`

value in the output.

### Values

a list containing the following components:

- x
- vector of sorted
`x`

values at which the estimate was computed. - y
- vector of density estimates at the corresponding
`x`

.

### Background

Density estimation is a smoothing operation. Inevitably there is a trade-off between bias in the estimate and the estimate's variability: large bandwidths will produce smooth estimates that may hide local features of the density; small bandwidths may introduce spurious bumps into the estimate.

### References

Wand, M. P. and Jones, M. C. (1995). *Kernel Smoothing.* Chapman and Hall, London.

### Examples

Documentation reproduced from package KernSmooth, version 2.23-10. License: Unlimited