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
______________________________________________
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PLEASE do read the posting guide
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--
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
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PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
