

   KKeerrnneell DDeennssiittyy EEssttiimmaattiioonn

        density(x, bw, adjust = 1, kernel="gaussian", window = kernel,
                n = 512, width, from, to, cut = 3, na.rm = FALSE)
        print(dobj)
        plot(dobj, main = NULL, xlab = NULL, ylab = "Density", type = "l",
             zero.line = TRUE, ...)

   AArrgguummeennttss::

          x: the data from which the estimate is to be com-
             puted.

          n: the number of equally spaced points at which the
             density is to be estimated.  When `n > 512', it is
             rounded up to the next power of 2 for efficieny
             reasons (`fft').

   kernel,window: a character string giving the smoothing ker-
             nel to be used.  This must be one of `"gaussian"',
             `"rectangular"', `"triangular"', or `"cosine"',
             and may be abbreviated to a single letter.

         bw: the smoothing bandwith to be used.  This is the
             standard deviation of the smoothing kernel.  It
             defaults to 0.9 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 (= Silverman's ``rule of thumb'').
             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' bandwidths beyond the extremes of the data.
             This allows the estimated density to drop to
             approximately zero at the extremes.

      na.rm: logical; if `TRUE', missing values are eliminated
             from `x' in advance to further computation.

       dobj: a ``density'' object.

   main, xlab, ylab, type: plotting parameters with useful
             defaults.

        ...: further plotting parameters.

   zero.line: logical; if `TRUE', add a base line at y = 0

   DDeessccrriippttiioonn::

        The function `density' computes kernel density esti-
        mates with the given kernel and bandwidth.

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

   DDeettaaiillss::

        The algorithm used in `density' disperses the mass of
        the empirical distribution function over a regular grid
        of at least 512 points and then uses the fast Fourier
        transform to convolve this approximation with a dis-
        cretized version of the kernel and then uses linear
        approximation to evaluate the density at the specified
        points.

   VVaalluuee::

        An object with class `"density"'.  The underlying
        structure is a list containing the following compo-
        nents.

          x: the `n' coordinates of the points where the den-
             sity 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.

     has.na: logical, indicating if there were `NA's in the
             sample and `na.rm == FALSE'.

   RReeffeerreenncceess::

        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 den-
        sity estimation.  J. Roy. Statist. Soc. B, 683-690.

   SSeeee AAllssoo::

        `convolve', `hist'.

   EExxaammpplleess::

        # 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))

