# bkde

##### Compute a Binned Kernel Density Estimate

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

- Keywords
- distribution, smooth

##### 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.

##### Value

a list containing the following components:

vector of sorted `x`

values at which the estimate was computed.

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.

##### See Also

##### Examples

```
# NOT RUN {
data(geyser, package="MASS")
x <- geyser$duration
est <- bkde(x, bandwidth=0.25)
plot(est, type="l")
# }
```

*Documentation reproduced from package KernSmooth, version 2.23-18, License: Unlimited*