[R] How to find maximum values on the density function of arandom variable

[guox at ucalgary.ca]

Yes, a random variable, discrete or continuous one, should associate with
a probability space and a measurable space.
I thought that graph of density(rv) below could give us an example of a
density function. I am very sorry for confusing you.

My question is how to find/estimate maximum values of a given density
function (even any given function within a given domain).
The number of these maximum values might be > 1 but the global one is unique.
Any ideas and references?
Thanks,
-james
> There is some considerable confusion in both the question and the reply.
>
> rv is **not**  a random variable. It is an (iid) sample from (i.e. a
> "realization" of) a random variable. It has *no* "density function" and
> the
> density() function is simply a procedure to **estimate** the density of
> the
> underlying random variable from which rv was sampled at a finite number
> of
> points. The result of density()and the max given in the reply will depend
> on
> the particular parameters given to density()(see ?density for details),
> as
> well as the data. In other words, both the question and answer posted are
> nonsense.
>
> Now let me contradict what I just said. **If** you consider rv a finite,
> discrete distribution (i.e. the whole population), then, in fact, it does
> have a discrete density, with point mass j(i)/n at each unique sample
> value
> i, where n is the total sample size (= 10000 in the example) and j(i) is
> the
> number of samples values == i, which would probably be 1 for all i. Then,
> of
> course, one can talk about the density of this finite distribution in the
> obvious way and its maximum or maxima, occur at those i for which n(i) is
> largest.
>
> But of course that's not what the poster really meant, so that brings us
> back to the nonsense question and answer. What James probably meant to
> ask
> was: "How can the maximum of the underlying population density function
> be
> estimated?" Well, that's a complicated issue. One could, of course, use
> some
> sort of density estimate -- there are tons -- and find its max; that was
> the
> approach taken in the answer, but it's not so simple as it appears
> because
> of the need to choose the **appropriate** estimate (including the
> parameters
> of the statistical algorithm doing the estimating ). This is the sort of
> thing that actually requires some careful thought and statistical
> expertise.
> You will find, I believe, that the prescription for finding the max
> suggested below can give quite different answers depending on the
> parameters
> chosen for this estimate, and on the estimate used. So if you need to do
> this right, may I suggest consulting the literature on density estimation
> or
> perhaps talking with your local statistician?
>
> -- Bert Gunter
> Genentech Nonclinical Statistics
>
> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
> On
> Behalf Of Mike Lawrence
> Sent: Thursday, March 12, 2009 5:40 PM
> To: guox at ucalgary.ca
> Cc: r-help at r-project.org
> Subject: Re: [R] How to find maximum values on the density function of
> arandom variable
>
> rv <- rbinom(10000,1,0.1) + rnorm(10000)
>
> d.rv = density(rv)
> d.x = d.rv$x
> d.y = d.rv$y
>
> d.rv.max = d.rv$x[which.max(d.rv$y)]
>
> plot(d.rv)
> abline(v=d.rv.max)
>
> #that what you want?
>
> On Thu, Mar 12, 2009 at 6:28 PM,  <guox at ucalgary.ca> wrote:
>> I would like to find the maximum values on the density function of a
>> random variable. For example, I have a random variable
>>
>> rv <- rbinom(10000,1,0.1) + rnorm(10000)
>>
>> Its density function is given by density(rv) and can be displayed by
>> plot(density(rv)). How to calculate its maximum values?
>> A density function may have a few (global and local) maximum values.
>> Please help. Thanks,
>> -james
>>
>> ______________________________________________
>> R-help at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>
>
>
> --
> Mike Lawrence
> Graduate Student
> Department of Psychology
> Dalhousie University
>
> Looking to arrange a meeting? Check my public calendar:
> http://tinyurl.com/mikes-public-calendar
>
> ~ Certainty is folly... I think. ~
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
>
>