R: Kernel distributions and random generation

dkernel {spatstat.core} | R Documentation

## 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 ≤ 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 Adrian.Baddeley@curtin.edu.au adrian@maths.uwa.edu.au

and Martin Hazelton

### See Also

`density.default`, `kernel.factor`

### 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)

[Package spatstat.core version 2.0-0 Index]