dkernel {spatstat.univar}

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 Baddeley [e-mail] and Martin Hazelton [e-mail].

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)