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
# }