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From: TideMan <mulgor@gmail.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: ecdf exists. why there is no epdf
Date: Thu, 9 Jun 2011 13:02:23 -0700 (PDT)
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On Jun 10, 4:40 am, "Roger Stafford"
<ellieandrogerxy...@mindspring.com.invalid> wrote:
> TideMan <mul...@gmail.com> wrote in message <a18b1a52-7bbe-44fb-a4ae-202af9a50...@s16g2000prf.googlegroups.com>...
> > On Jun 9, 5:51 pm, "Alex " <ala...@yahoo.com> wrote:
> > > Dear all,
> > > I would like to ask you something concerning ecdf.
> > > I think I miss something from the theory.
> > > Why there is ecdf and there is no something like epdf. Empirical pdf.
> > > Best Regards
> > > Alex
>
> > And now you've started yet another thread on the same topic.
> > WARNING: this person has started 3 different threads on exactly the
> > same topic.
> > In response to the first thread, he was told all he needs to know, but
> > he has chosen to ignore this.
> > This guy's wasting our time.
>
> - - - - - - - - - - - -
>   Tideman, I think Alex is asking a legitimate question and it deserves a straight answer.
>
>   In answer to your question, Alex, with empirical data it is relatively easy to produce a cumulative distribution curve from it that looks reasonably close to the true underlying distribution.  It amounts to little more than sorting the data.
>
>   Exhibiting a valid density distribution approximation is more difficult.  One would be trying to deduce the derivative or slope of this same curve.  Unfortunately, unless there is an enormous amount of data furnished, the cumulative curve has a markedly jagged appearance and all estimates of density are bound to be highly inaccurate.  The reluctance of Mathworks to write routines that could give extremely inaccurate results is understandable, though if the appropriate filtering and/or interpolation were done it is something that could give smooth-looking, though perhaps still inaccurate, results.
>
>   As you may be aware, using purely empirical results to demonstrate reliably that a given process has a certain probability distribution is an undertaking that requires an enormous amount of data even for a single variable.  For more than one variable it becomes very much more difficult to achieve empirically and often has to be supported by other types of evidence or arguments.
>
> Roger Stafford

Well, for a mere engineer who deals with real physical data, the
empirical PDF is simply the histogram, as I pointed out to OP in his
original thread.
Integrating the PDF using cumsum produces the empirical CDF.
You have lots of freedom in choosing the bins for the histogram and
this governs how smooth the CDF is.