\name{dkde, pkde, qkde, rkde}\alias{dkde}\alias{pkde}\alias{qkde} \alias{rkde} \title{Functions for 1-dimensional kernel density estimates} \description{   Functions for 1-dimensional kernel density estimates. } \usage{ pkde(q, fhat) qkde(p, fhat) dkde(x, fhat) rkde(n, fhat, positive=FALSE) } \arguments{   \item{x,q}{vector of quantiles}   \item{p}{vector of probabilities}   \item{n}{number of observations}   \item{positive}{flag to compute KDE on the positive real	 line. Default is FALSE.}    \item{fhat}{kernel density estimate, object of class \code{"kde"}} } \value{   For the kernel density estimate \code{fhat},   \code{pkde} computes the cumulative probability for the quantile   \code{q}, \code{qkde} computes the quantile corresponding to the probability   \code{p}, \code{dkde} computes the density value at   \code{x} and \code{rkde} computes a random sample of size \code{n}.    }\details{   \code{pkde} uses the Simpson's rule is used for the numerical  integration.  %So shares the limitations of this numerical method. %\code{dkde} is a  %shortcut for \code{kde(x=fhat$x, h=fhat$h,  %eval.points=fhat$x)$estimate}.  \code{rkde} uses  Silverman (1986)'s method to generate a random sample from a KDE.}\references{ Silverman, B. (1986) \emph{Density Estimation for Statistics and  Data Analysis}. Chapman \& Hall/CRC. London.}\examples{x <- rnorm.mixt(n=10000, mus=0, sigmas=1, props=1)fhat <- kde(x=x, h=hpi(x))p1 <- pkde(fhat=fhat, q=c(-1, 0, 0.5))qkde(fhat=fhat, p=p1)     ## should be close to c(-1, 0, 0.5)x1 <- rkde(fhat, n=100)plot(fhat)fhat1 <- kde(x=x1, h=hpi(x1))plot(fhat1, add=TRUE, col=2)fhat2 <- dkde(x=x1, fhat=fhat1)points(x1, fhat2, col=3)}\keyword{ smooth}