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\name{density2d}
\alias{density2d}
\alias{grid2d}
\alias{density2d}
\alias{hist2d}
\alias{integrate2d}
\title{Bivariate Density Tools}
\description{
Grid generator, kernel density estimator,
histogram counter, and integrator for
bivariate distributions
}
\usage{
grid2d(x = (0:10)/10, y = x)
density2d(x, y = NULL, n = 20, h = NULL, limits = c(range(x), range(y)))
hist2d(x, y = NULL, n = c(20, 20))
integrate2d(fun, error = 1.0e-5, \dots)
}
\arguments{
\item{error}{
the error bound to be achieved by the integration formula.
A numeric value.
}
\item{fun}{
the function to be integrated. The first argument requests
the x values, the second the y values, and the remaining
are reserved for additional parameters. The integration is
over the unit square "[0,1]\^2".
}
\item{h}{
a vector of bandwidths for \code{x} and \code{y} directions.
Defaults to normal reference bandwidth.
}
\item{limits}{
the limits of the rectangle covered by the grid.
}
\item{n}{
n - an integer specifying the number of grid points in each
direction. The default value is 20.\cr
[hist2D] - \cr
In this case \code{n} may be a scalar or a two element vector.
The default value is 20.\cr
[rnorm2d] - \cr
the number of random deviates to be generated, an integer value.
}
\item{x, y}{
two numeric vectors defining the x and y coordinates. \cr
[density2D][hist2D] - \cr
two vectors of coordinates of data. If \code{y} is NULL then
\code{x} is assumed to be a two column matrix, where the first
column contains the \code{x} data, and the second column the
\code{y} data.
}
\item{\dots}{
parameters passed to the function to be integrated.
}
}
\value{
\code{grid2d}
\cr
returns a list with two vectors named \code{$x} and \code{$y} spanning
the grid defined by the coordinate vectors \code{x} and \code{y}.
\code{density2d}\cr
\code{hist2d}
\cr
returns a list with three elements \code{$x}, \code{$y}, and
\code{$z}. \code{x} and \code{y} are vectors spanning the two
dimensional grid and \code{z} the corresponding matrix. The
output can directly serve as input to the plotting functions
\code{image}, \code{contour} and \code{persp}.
\code{integrate2d}
\cr
returns a list with the \code{$value} of the integral over the
unit square [0,1]\^2, an \code{$error} estimate and the number
of grid \code{$points} used by the integration function.
}
\references{
Azzalini A., (2004);
\emph{The sn Package};
R Reference Guide available from www.r-project.org.
Venables W.N., Ripley B.D., (2002);
\emph{Modern Applied Statistics with S},
Fourth Edition, Springer.
Warnes G.R., (2004);
\emph{The gregmisc Package};
R Reference Guide available from www.r-project.org.
}
\author{
W.N. Venables and B.D. Ripley for the underlying kde2d function, \cr
Gregory R. Warnes for the underlying hist2d function, \cr
Diethelm Wuertz for the Rmetrics \R-port.
}
\keyword{math}
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