dkernel: Kernel distributions and random generation

In spatstat.univar: One-Dimensional Probability Distribution Support for the 'spatstat' Family

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

x, q	Vector of quantiles.
p	Vector of probabilities.
kernel	String name of the kernel. Options are "gaussian", "rectangular", "triangular", "epanechnikov", "biweight", "cosine" and "optcosine". (Partial matching is used).
n	Number of observations.
mean	Mean of distribution.
sd	Standard deviation of distribution.
lower.tail	logical; if TRUE (the default), then probabilities are P(X \le x), otherwise, 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 density.default, namely "gaussian", "rectangular", "triangular", "epanechnikov", "biweight", "cosine" and "optcosine". For more information about these kernels, see density.default.

dkernel gives the probability density, pkernel gives the cumulative distribution function, qkernel gives the quantile function, and rkernel generates random deviates.

Value

A numeric vector. For dkernel, a vector of the same length as x containing the corresponding values of the probability density. For pkernel, a vector of the same length as x containing the corresponding values of the cumulative distribution function. For qkernel, a vector of the same length as p containing the corresponding quantiles. For rkernel, a vector of length n containing randomly generated values.

Author(s)

\adrian

and \martinH.

See Also

density.default, kernel.factor, kernel.moment, kernel.squint.

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)

spatstat.univar documentation built on June 8, 2025, 12:52 p.m.