RtoDPQ {distr}

Default procedure to fill slots d,p,q given r for a.c. distributions

Description

function to do get empirical density, cumulative distribution and quantile function from random numbers

Usage

RtoDPQ(r, e = getdistrOption("RtoDPQ.e"), 
       n = getdistrOption("DefaultNrGridPoints"), y = NULL)

Arguments

r

the random number generator

e

10^e numbers are generated, a higher number leads to a better result.

n

The number of grid points used to create the approximated functions, a higher number leads to a better result.

y

a (numeric) vector or NULL

Details

RtoDPQ generates 10^e random numbers, by default

e = RtoDPQ.e

. Instead of using simulated grid points, we have an optional parameter y for using N. Horbenko's quantile trick: i.e.; on an equally spaced grid x.grid on [0,1], apply f(q(x)(x.grid)) and write the result to y and produce density and cdf from this value y given to RtoDPQ as argument (instead of simulating grid points).

The density is formed on the basis of n points using approxfun and density, by default

n = DefaultNrGridPoints

. The cumulative distribution function and the quantile function are also created on the basis of n points using approxfun and ecdf. Of course, the results are usually not exact as they rely on random numbers.

Value

RtoDPQ returns a list of functions.

dfun

density

pfun

cumulative distribution function

qfun

quantile function

Note

Use RtoDPQ for absolutely continuous and RtoDPQ.d for discrete distributions.

Author(s)

Thomas Stabla [e-mail],
Florian Camphausen [e-mail],
Peter Ruckdeschel [e-mail],
Matthias Kohl [e-mail]

See Also

UnivariateDistribution-class, density, approxfun, ecdf

Examples

set.seed(20230508)
rn2 <- function(n){rnorm(n)^2}
x <- RtoDPQ(r = rn2, e = 4, n = 512)
# returns density, cumulative distribution and quantile function of
# squared standard normal distribution
## IGNORE_RDIFF_BEGIN
x$dfun(4)
RtoDPQ(r = rn2, e = 5, n = 1024) # for a better result
## IGNORE_RDIFF_END
rp2 <- function(n){rpois(n, lambda = 1)^2}
x <- RtoDPQ.d(r = rp2, e = 5)
# returns density, cumulative distribution and quantile function of
# squared Poisson distribution with parameter lambda=1