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.
