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-boun...@r-project.org [mailto:r-help-boun...@r-project.org] > On > Behalf Of Mike Lawrence > Sent: Thursday, March 12, 2009 5:40 PM > To: g...@ucalgary.ca > Cc: r-help@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, <g...@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@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@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. > > > ______________________________________________ R-help@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.
