Implementation of d/p/q/r functions for xDensity distributions.

Source: R/xDensity.R

Implementation of d/p/q/r functions for xDensity distributions.

dXD(x, xDens, log = FALSE)

pXD(q, xDens, lower.tail = TRUE, log.p = FALSE)

qXD(p, xDens, lower.tail = TRUE, log.p = FALSE)

rXD(n, xDens)

Arguments

x, q

Vector of quantiles.
xDens

Object of class xDensity representing the distribution.
log, log.p

Logical; if TRUE, probabilities p are given as log(p).
lower.tail

Logical; if TRUE (default), probabilities are P[X <= x] otherwise, P[X > x].
p

Vector of probabilities.
n

Number of observations.

Value

For the underlying xDensity object, dXD gives the density, pXD gives the distribution function, qXD gives the quantile function and rXD generates n random values.

Details

Extended density (or xDensity) objects provide a compact representation of arbitrary one-dimensional distributions defined on the real line. That is, an xDensity object is a list with the following elements:

  • xrng, ndens: range and number of gridpoints defining the main density region, i.e. xseq = seq(xrng[1], xrng[2], len = xn).

  • ypdf, ylpdf, ycdf: density, log-density, and cdf on the grid.

  • mean, sd: mean and standard deviation of a Normal distribution to use outside the specified density range.

See also

matrixXD, kernelXD, gc4XD for various xDensity object constructors.

Examples

# xDensity representation of a N(0,1) distribution

# construct the xDensity object using the known PDF dnorm
xseq <- seq(-4, 4, len = 500) # where to evaluate density
xDens <- matrixXD(cbind(xseq, dnorm(xseq)))

# check random sampling
x <- rXD(1e5, xDens = xDens)
hist(x, breaks = 100, freq = FALSE)
curve(dnorm, add = TRUE, col = "red")

# check PDF
x <- rnorm(5)
rbind(true = dnorm(x, log = TRUE), xDens = dXD(x, xDens, log = TRUE))
#>            [,1]      [,2]      [,3]      [,4]      [,5]
#> true  -1.000109 -1.369717 -1.711516 -1.009958 -1.770372
#> xDens -1.002504 -1.373909 -1.710871 -1.009187 -1.772558

# check CDF
rbind(true = pnorm(x, log = TRUE), xDens = pXD(x, xDens, log = TRUE))
#>            [,1]       [,2]      [,3]      [,4]      [,5]
#> true  -1.068552 -0.1877551 -2.263269 -1.094182 -2.343858
#> xDens -1.068550 -0.1877586 -2.263223 -1.094173 -2.343812

# check inverse-CDF
probs <- runif(5)
rbind(true = qnorm(probs), xDens = qXD(probs, xDens))
#>             [,1]      [,2]      [,3]      [,4]        [,5]
#> true  -0.1932449 0.8129345 0.5756194 0.3169434 -0.07806913
#> xDens -0.1932441 0.8129474 0.5756196 0.3169472 -0.07806937