[R] calculate quantiles of a custom function

[Bert Gunter]

Gerhard:

Strictly speaking, it's quantiles of a custom "distribution", not function.

There may be some way to handle your example easily, but, in general,
you would need to solve the resulting integral equation. This is hard
-- closed form solutions rarely exist; good approximations require
work.

So a standard approach is: simulate. Indeed, many simulation tricks
(under the rubric of "variance reduction") have been developed exactly
for such monte carlo integration. Consult a good reference or
knowledgeable person for details.

-- Bert

On Tue, Jan 3, 2012 at 4:24 AM, Gerhard <feldspat at gmx.net> wrote:
> Hi,
>
> I guess that my problem has an obvious answer, but I have not been able to
> find it.
>
> Suppose I create a custom function, consisting of two beta-distributions:
>
> myfunction <- function(x) {
>  dbeta(x,2,6) + dbeta(x,6,2)
> }
>
> How can I calculate the quantiles of myfunction?
>
> I have not seen any continous function treated in the docs, and applying the
> "quantile function" gives me an error (since it seems only to be defined on
> lists and atoms).
>
> Thank you in advance,
>
> Gerhard
>
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-- 

Bert Gunter
Genentech Nonclinical Biostatistics

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