# [BioC] RMA biomodality, distribution and transformation

Benjamin Otto b.otto at uke.uni-hamburg.de
Fri Jan 25 15:39:51 CET 2008

```Dear bioconductors,

some time ago in one of the discussion about RMA-bimodality Wolfgang
Huber and Peter Warren pointed out, that a similar distribution could be
simulated with

> n <- 10000
> z = 20 + exp(c(rnorm(n), 3+rnorm(n)))
> plot(density(log2(z)))

Now here comes a more mathematical question. Suppose the following

> x0 <- rnorm(n)
> x1 <- x0 + 3

It is quite easy to get the same density in two ways:

for x0 it's super easy:
> plot(density(x0))
> plot(x0,dnorm(x0))

and for x1 it's still intuitive:
> plot(density(x1))
> plot(x1,dnorm(x1 - 3))

That's because we are currently only shifting the distribution. But how
do I transform the x-values for y-value calculation via dnorm() when
applying the more complex exponential function?

> x2 <- exp(x0)
> plot(density(x2))
> plot(x2, ..???..)

best regards

Benjamin

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