Random generation from univariate kernel density
Random generation from univariate kernel density
ruvk(
n,
y,
bw = bw.nrd0(y),
kernel = c("gaussian", "epanechnikov", "rectangular", "triangular", "biweight",
"cosine", "optcosine"),
weights = NULL,
adjust = 1,
shrinked = FALSE
)n |
number of observations. If |
y |
numeric vector. |
bw |
the smoothing bandwidth to be used. The kernels are scaled
such that this is the standard deviation of the smoothing
kernel (see |
kernel |
a character string giving the smoothing kernel to be used. This must partially match one of "gaussian", "rectangular", "triangular", "epanechnikov", "biweight", "cosine" or "optcosine", with default "gaussian", and may be abbreviated. |
weights |
numeric vector of length equal to |
adjust |
scalar; the bandwidth used is actually |
shrinked |
if |
Univariate kernel density estimator is defined as
f(x) = sum[i](w[i] * Kh(x-y[i]))
where w is a vector of weights such that all w[i] ≥ 0 and sum(w) = 1 (by default uniform 1/n weights are used), Kh = K(x/h)/h is kernel K parametrized by bandwidth h and y is a vector of data points used for estimating the kernel density.
For estimating kernel densities use the density function.
The random generation algorithm is described in the documentation of
kernelboot function.
Deng, H. and Wickham, H. (2011). Density estimation in R. http://vita.had.co.nz/papers/density-estimation.pdf
# ruvk() produces samples from kernel densities as estimated using
# density() function from base R
hist(ruvk(1e5, mtcars$mpg), 100, freq = FALSE, xlim = c(5, 40))
lines(density(mtcars$mpg, bw = bw.nrd0(mtcars$mpg)), col = "red")
# when using 'shrinked = TRUE', the samples differ from density() estimates
# since they are shrinked to have the same variance as the underlying data
hist(ruvk(1e5, mtcars$mpg, shrinked = TRUE), 100, freq = FALSE, xlim = c(5, 40))
lines(density(mtcars$mpg, bw = bw.nrd0(mtcars$mpg)), col = "red")
# Comparison of different univariate kernels under standard parametrization
kernels <- c("gaussian", "epanechnikov", "rectangular", "triangular",
"biweight", "cosine", "optcosine")
partmp <- par(mfrow = c(2, 4), mar = c(3, 3, 3, 3))
for (k in kernels) {
hist(ruvk(1e5, 0, 1, kernel = k), 25, freq = FALSE, main = k)
lines(density(0, 1, kernel = k), col = "red")
}
par(partmp)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.