Compute a Binned Kernel Density Estimate - R Documentation

`bkde` Compute a Binned Kernel Density Estimate

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`	length-one logical vector: 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:

`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

data(geyser, package="MASS")
x <- geyser$duration
est <- bkde(x, bandwidth=0.25)
plot(est, type="l")

bkde Compute a Binned Kernel Density Estimate