dkernel.Rd
\name{dkernel}
\alias{dkernel}
\alias{pkernel}
\alias{qkernel}
\alias{rkernel}
\title{Kernel distributions and random generation}
\description{Density, distribution function, quantile function and random
generation for several distributions used in kernel estimation
for numerical data.
}
\usage{
dkernel(x, kernel = "gaussian", mean = 0, sd = 1)
pkernel(q, kernel = "gaussian", mean = 0, sd = 1, lower.tail = TRUE)
qkernel(p, kernel = "gaussian", mean = 0, sd = 1, lower.tail = TRUE)
rkernel(n, kernel = "gaussian", mean = 0, sd = 1)
}
\arguments{
\item{x, q}{Vector of quantiles.}
\item{p}{Vector of probabilities.}
\item{kernel}{
String name of the kernel.
Options are
\code{"gaussian"}, \code{"rectangular"},
\code{"triangular"},
\code{"epanechnikov"},
\code{"biweight"},
\code{"cosine"} and \code{"optcosine"}.
(Partial matching is used).
}
\item{n}{Number of observations.}
\item{mean}{Mean of distribution.}
\item{sd}{Standard deviation of distribution.}
\item{lower.tail}{logical; if \code{TRUE} (the default),
then probabilities are \eqn{P(X \le x)}{P[X \le x]},
otherwise, \eqn{P(X > x)}.
}
}
\details{
These functions give the
probability density, cumulative distribution function,
quantile function and random generation for several
distributions used in kernel estimation for one-dimensional
(numerical) data.
The available kernels are those used in \code{\link[stats]{density.default}},
namely \code{"gaussian"}, \code{"rectangular"},
\code{"triangular"},
\code{"epanechnikov"},
\code{"biweight"},
\code{"cosine"} and \code{"optcosine"}.
For more information about these kernels,
see \code{\link[stats]{density.default}}.
\code{dkernel} gives the probability density,
\code{pkernel} gives the cumulative distribution function,
\code{qkernel} gives the quantile function,
and \code{rkernel} generates random deviates.
}
\value{
A numeric vector.
For \code{dkernel}, a vector of the same length as \code{x}
containing the corresponding values of the probability density.
For \code{pkernel}, a vector of the same length as \code{x}
containing the corresponding values of the cumulative distribution function.
For \code{qkernel}, a vector of the same length as \code{p}
containing the corresponding quantiles.
For \code{rkernel}, a vector of length \code{n}
containing randomly generated values.
}
\examples{
x <- seq(-3,3,length=100)
plot(x, dkernel(x, "epa"), type="l",
main=c("Epanechnikov kernel", "probability density"))
plot(x, pkernel(x, "opt"), type="l",
main=c("OptCosine kernel", "cumulative distribution function"))
p <- seq(0,1, length=256)
plot(p, qkernel(p, "biw"), type="l",
main=c("Biweight kernel", "cumulative distribution function"))
y <- rkernel(100, "tri")
hist(y, main="Random variates from triangular density")
rug(y)
}
\seealso{
\code{\link[stats]{density.default}},
\code{\link{kernel.factor}}
}
\author{\adrian
\email{adrian@maths.uwa.edu.au}
and Martin Hazelton
}
\keyword{methods}
\keyword{nonparametric}
\keyword{smooth}