# [R] Any packages or ways available providing un-/a-/non-symmetric centered distributions?

Paul Menzel paulepanter at users.sourceforge.net
Sun Dec 11 10:43:01 CET 2011

```Dear R folks,

I would like to use un-/a-/non-symmetric centered, i. e. the expectation
vanishes/is zero, distributions.

Searching for that is not that easy since all three words un-, a-,
non-symmetric seem to be common.

Do I need to create such a distribution myself by for example composing
a distribution?

I would use `sample()` and for integer-valued the following would be one
example. The expectation vanishes too, 1/4 * (-4 - 1 + 2 + 3) = 0.

> x = sample(c(-4L, -1L, 2L, 3L))
> y = sample(c(-4L, -1L, 2L, 3L), 1e7, replace=TRUE); mean(y)
[1] 0.0006821
> # replicate will produce a matrix, but in this case it should not matter for the mean
> x = replicate(2, sample(c(-4L, -1L, 2L, 3L), replace=TRUE)); x
[,1] [,2]
[1,]   -1    2
[2,]    3   -1
[3,]    3   -1
[4,]   -1    3
> mean(x)
[1] 0.875
> # Passing the length explicitly to `sample()` as a work around.
> x = replicate(1e1, sample(c(-4L, -1L, 2L, 3L), 1, replace=TRUE)); x
[1] -4  2  2  3 -4 -4  2  2  2  2

For continues (without 0) distributions I came up with the following.

> # -rexp(1, 2) has expectation -1.
> # sqrt(pi/2) * abs(rnorm(1))
> # http://en.wikipedia.org/wiki/Half-normal_distribution
> # X ~ N(0, 1) ⇒ E(|X|) = √(2/π)
> x = sample(c(sqrt(pi/2) * abs(rnorm(1)), -rexp(1, 1)), 1); x
[1] 0.2730692

Without passing `, 1` as the length to `sample` I would get two values.

> x = sample(c(sqrt(pi/2) * abs(rnorm(1)), -rexp(1, 1))); x
[1] -0.4055199  1.8830235

Wanting to use `replicate()` therefore the explicit length for
`sample()` should be passed here too.

> x = replicate(1e5, sample(c(sqrt(pi/2) * abs(rnorm(1)), -rexp(1, 1)), 1)); mean(x)
[1] -0.001099127

Are there other sophisticated ways to create such distributions easily?

Thanks,

Paul
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