bkde               package:KernSmooth               R Documentation

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 = 401, range.x, truncate = TRUE)

Arguments:

       x: 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. 

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:

       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.

See Also:

     'density', 'dpik', 'hist', 'ksmooth'.

Examples:

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

