# RtoDPQ.LC

##### 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

- Keywords
- distribution, arith, math

##### 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.

##### concept

- random sample
- image distribution
- absolutely continuous distribution
- utility

##### See Also

##### Examples

```
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)
```

*Documentation reproduced from package distr, version 2.6, License: LGPL-3*