# RtoDPQ

0th

Percentile

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

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

Keywords
distribution, arith, math
##### 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.

UnivariateDistribution-class, density, approxfun, ecdf

• RtoDPQ
##### Examples
# NOT RUN {
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
x\$dfun(4)
RtoDPQ(r = rn2, e = 5, n = 1024) # for a better result

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
# }

Documentation reproduced from package distr, version 2.8.0, License: LGPL-3

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