If you are trying to build your own function then presumably you do
not want the global maximum, since that is trivially returned by max.
So what do you really want? Is this a programming question or just a
general statistics question?
If you want to search along a (specific) sequence for local maxima,
then you could try programming with "second differences" looking for
shifts in sign from positive to negative.
vec <- c(1:5, 6, 5:1)
[1] 0 0 0 0 -2 0 0 0 0
It is a bit ambiguous what you would do with this vector:
> vec2 <- c(1:5,rep(6,3),5:1)
> diff(diff(vec2))
[1] 0 0 0 0 -1 0 -1 0 0 0 0
--
David Winsemius
On Mar 13, 2009, at 12:48 PM, guox at ucalgary.ca wrote:
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