## Kernel Density Estimation

## Usage

    density(x, bw, adjust = 1, kernel="gaussian", window = kernel,
            n = 512, width, from, to, cut = 3, na.rm = FALSE)

    print(dobj)
    plot(dobj, ...)

## Arguments

`x` | the values for which the estimate is to be computed.
`n` | the number of equally spaced points at which the density is to be estimated. This is rounded up to the next power of 2, with a minimum value of 512.
`kernel,window` | a character string giving the smoothing kernel to be used. This must be one of `"gaussian"`, `"rectangular"`, `"triangular"`, or `"cosine"`, and may be abbrevited to a single letter.
`bw` | the smoothing bandwith to be used. This is the standard deviation of the smoothing kernel. It defaults to 1.06 times the minimum of the standard deviation and the interquartile range divided by 1.34 times the sample size to the negative one fifth power. The specified value of `bw` is multiplied by `adjust`.
`adjust` | the bandwith used is actually `adjust*bw`. This makes it easy to specify values like ``half the default'' bandwidth.
`width` | this exists for compatibility with S.
`from,to` | the left and right-most points of the grid at which the density is to be estimated.
`cut` | by default, the values of `left` and `right` are `cut` bandwiths beyond the extremes of the data.
`na.rm` | logical; if `TRUE`, missing values are eliminated from `x` in advance to further computation.
`dobj` | a ``density'' object.
`...` | plotting parameters.

## Description

The function `density` computes kernel density estimates with the given kernel and bandwidth (which is the standard deviation of the kernel).

The generic functions `plot` and `print` have methods for density objects.

The algorithm used in `density` disperses the mass of the empirical distribution function over a regular grid and then uses the fast Fourier transform to convolve this approximation with a discretized version of the kernel.

## Value

An object with class ``density''. The underlying structure is a list containing the following components.

`x` | the coordinates of the points where the density is estimated.
`y` | the estimated density values.
`bw` | the bandwidth used.
`n` | the sample size `length(x)`.
`call` | the call which produced the result.
`data.name` | the deparsed name of the `x` argument.

## References

Silverman, B. W. (1986). Density Estimation. London: Chapman and Hall.

Venables, W. N. and B. D. Ripley (1994). Modern Applied Statistics with S-Plus. New York: Springer.

Scott, D. W. (1992). Multivariate Density Estimation. Theory, Practice and Visualization. New York: Wiley.

Sheather, S. J. and M. C. Jones (1991). ``A reliable data-based bandwidth selection method for kernel density estimation. J. Roy. Statist. Soc. B, 683-690.

## See Also

`convolve`, `hist`.

## Examples

    # The Old Faithful geyser data
    data(faithful)
    d <- density(faithful$eruptions, bw=0.15)
    d
    plot(d)

    plot(d, type="n")
    polygon(d, col="wheat")

    ## Missing values:
    x <- xx <- faithful$eruptions
    x[i.out <- sample(length(x), 10)] <- NA
    doR <- density(x, bw=0.15, na.rm = TRUE)
    doN <- density(x, bw=0.15, na.rm = FALSE)
    lines(doR, col="blue")
    lines(doN, col="red")
    points(xx[i.out], rep(.01,10))

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