Default procedure to fill slots d,p,q given r for Lebesgue decomposed distributions
function to do get empirical density, cumulative distribution and quantile function from random numbers
the random number generator
10^e numbers are generated, a higher number leads to a better result.
The number of grid points used to create the approximated functions, a higher number leads to a better result.
a (numeric) vector or
RtoDPQ.LC generates 10^e random numbers, by default
e = RtoDPQ.e
Replicates are assumed to be part of the discrete part, unique values to be
part of the a.c. part of the distribution. For the replicated ones,
we generate a discrete distribution by a call to
For the a.c. part, similarly to
RtoDPQ we have an optional parameter
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)), write the result to
y and use these
values instead of simulated ones.
The a.c. density is formed on the basis of n points using approxfun and density (applied to the unique values), by default
n = DefaultNrGridPoints
The cumulative distribution function is based on all random variables,
and, as well as the quantile function, is also created on the basis of n points using
ecdf. Of course, the results are usually not exact as they rely on random numbers.
RtoDPQ.LC returns an object of class
RtoDPQ for absolutely continuous and
RtoDPQ.d for discrete distributions.
Peter Ruckdeschel email@example.com
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rn2 <- function(n)ifelse(rbinom(n,1,0.3),rnorm(n)^2,rbinom(n,4,.3)) x <- RtoDPQ.LC(r = rn2, e = 4, n = 512) plot(x) # returns density, cumulative distribution and quantile function of # squared standard normal distribution d.discrete(x)(4) x2 <- RtoDPQ.LC(r = rn2, e = 5, n = 1024) # for a better result plot(x2)
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