# RtoDPQ.LC: Default procedure to fill slots d,p,q given r for Lebesgue...

### Description

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

### Usage

 ```1 2``` ```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

 ```1 2 3 4 5 6 7 8``` ```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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