RtoDPQ
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.
density
cumulative distribution function
quantile function
Note
Use RtoDPQ
for absolutely continuous and RtoDPQ.d
for discrete distributions.
See Also
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
# }