RtoDPQ.LC {distr} R Documentation

## Default procedure to fill slots d,p,q given r for Lebesgue decomposed distributions

### Description

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

### Usage

RtoDPQ.LC(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.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 DiscreteDistribution.

For the a.c. part, similarly to RtoDPQ 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)), 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 approxfun and ecdf. Of course, the results are usually not exact as they rely on random numbers.

### Value

RtoDPQ.LC returns an object of class UnivarLebDecDistribution.

### Note

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

### Author(s)

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

UnivariateDistribution-class, density, approxfun, ecdf

### Examples

set.seed(20230508)
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
## IGNORE_RDIFF_BEGIN
d.discrete(x)(4)
## IGNORE_RDIFF_END
x2 <- RtoDPQ.LC(r = rn2, e = 5, n = 1024) # for a better result
plot(x2)


[Package distr version 2.9.3 Index]