R help - Mar 2019 - density vs. mass for discrete probability functions

Dear R users,

While experimenting with the dbinom() function and reading its
documentation (?dbinom) it reads that "dbinom gives the density" but
shouldn't it be called "mass" instead of "density"? I
assume that it
has something to do with keeping the function for "density" consistent
across discrete and continuous probability functions - but I am not
sure and was hoping someone could clarify?

Furthermore the help file for dbinom() function references a link
(http://www.herine.net/stat/software/dbinom.html) but it doesn't seem
to land where it should. Maybe this could be updated?

Thank you,
Stefan

On 2019-03-14 19:43, Stefan Schreiber wrote:
> Dear R users,
>
> While experimenting with the dbinom() function and reading its
> documentation (?dbinom) it reads that "dbinom gives the density"
but
> shouldn't it be called "mass" instead of "density"?
I assume that it
> has something to do with keeping the function for "density"
consistent
> across discrete and continuous probability functions - but I am not
> sure and was hoping someone could clarify?

 ????? The Wikipedia article on "Probability density function" gives
the
"Formal definition" that, "the density of [a random variable]
with
respect to a reference measure ... is the Radon?Nikodym derivative".


 ????? This sounds bazaar to people who haven't studied 
measure-theoretic probability, but it allows a unified treatment of 
continuous and discrete probabilities and to others that are 
combinations and neither.? The "reference measure" for a discrete 
probability distribution is the "counting measure", which supports the
use of the word "density" in this context being equivalent to
"mass".?
For continuous distributions, the "reference measure" is routinely
taken
to be the "improper prior" that assigns measure 1 to any unit interval
on the real line.


 ????? Does that make it clear as mud?


 ????? Spencer Graves


https://en.wikipedia.org/wiki/Probability_density_function
>
> Furthermore the help file for dbinom() function references a link
> (http://www.herine.net/stat/software/dbinom.html) but it doesn't seem
> to land where it should. Maybe this could be updated?
>
> Thank you,
> Stefan
>
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> 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.

Mathematically, you can bring discrete and continuous distributions on a common
footing by defining probability functions as densities wrt. counting measure.
You don't really need Radon-Nikodym derivatives to understand the idea, just
the fact that sums can be interpreted as integrals wrt counting measure, hence
sum_{x in A} f(x) and int_A f(x) dx are essentially the same concept.

-pd
> On 15 Mar 2019, at 01:43 , Stefan Schreiber <sschreib at ualberta.ca>
wrote:
> 
> Dear R users,
> 
> While experimenting with the dbinom() function and reading its
> documentation (?dbinom) it reads that "dbinom gives the density"
but
> shouldn't it be called "mass" instead of "density"?
I assume that it
> has something to do with keeping the function for "density"
consistent
> across discrete and continuous probability functions - but I am not
> sure and was hoping someone could clarify?
> 
> Furthermore the help file for dbinom() function references a link
> (http://www.herine.net/stat/software/dbinom.html) but it doesn't seem
> to land where it should. Maybe this could be updated?
> 
> Thank you,
> Stefan
> 
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> 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.
-- 
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Office: A 4.23
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com

Thank you Peter and Spencer. That clears things up. Also since no one
responded the second part of my question, I'm still wondering if it was
noted that there is a hyperlink in the dbinom help file (?dbinom) that
isn't directing correctly?

Stefan

On Fri, Mar 15, 2019, 07:37 peter dalgaard, <pdalgd at gmail.com> wrote:
> Mathematically, you can bring discrete and continuous distributions on a
> common footing by defining probability functions as densities wrt. counting
> measure. You don't really need Radon-Nikodym derivatives to understand
the
> idea, just the fact that sums can be interpreted as integrals wrt counting
> measure, hence sum_{x in A} f(x) and int_A f(x) dx are essentially the same
> concept.
>
> -pd
>
> > On 15 Mar 2019, at 01:43 , Stefan Schreiber <sschreib at
ualberta.ca>
> wrote:
> >
> > Dear R users,
> >
> > While experimenting with the dbinom() function and reading its
> > documentation (?dbinom) it reads that "dbinom gives the
density" but
> > shouldn't it be called "mass" instead of
"density"? I assume that it
> > has something to do with keeping the function for "density"
consistent
> > across discrete and continuous probability functions - but I am not
> > sure and was hoping someone could clarify?
> >
> > Furthermore the help file for dbinom() function references a link
> > (http://www.herine.net/stat/software/dbinom.html) but it doesn't
seem
> > to land where it should. Maybe this could be updated?
> >
> > Thank you,
> > Stefan
> >
> > ______________________________________________
> > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> > 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.
>
> --
> Peter Dalgaard, Professor,
> Center for Statistics, Copenhagen Business School
> Solbjerg Plads 3, 2000 Frederiksberg, Denmark
> Phone: (+45)38153501
> Office: A 4.23
> Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com
>
>
>
>
>
>
>
>
>
>
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On 2019-03-15 08:37, peter dalgaard wrote:
> Mathematically, you can bring discrete and continuous distributions on a
common footing by defining probability functions as densities wrt. counting
measure. You don't really need Radon-Nikodym derivatives to understand the
idea, just the fact that sums can be interpreted as integrals wrt counting
measure, hence sum_{x in A} f(x) and int_A f(x) dx are essentially the same
concept.

 ????? Correct.? That's for clearing up my "mud".?
sg
> -pd
>
>> On 15 Mar 2019, at 01:43 , Stefan Schreiber <sschreib at
ualberta.ca> wrote:
>>
>> Dear R users,
>>
>> While experimenting with the dbinom() function and reading its
>> documentation (?dbinom) it reads that "dbinom gives the
density" but
>> shouldn't it be called "mass" instead of
"density"? I assume that it
>> has something to do with keeping the function for "density"
consistent
>> across discrete and continuous probability functions - but I am not
>> sure and was hoping someone could clarify?
>>
>> Furthermore the help file for dbinom() function references a link
>> (http://www.herine.net/stat/software/dbinom.html) but it doesn't
seem
>> to land where it should. Maybe this could be updated?
>>
>> Thank you,
>> Stefan
>>
>> ______________________________________________
>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
>> 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.

Stefan---

Under the measure-theoretic approach to probability, discrete & continuous 
probability densities follow the same underlying mathematical principles.
Check any text on measure-theoretic probability theory.

---JFL





Stefan Schreiber <sschreib at ualberta.ca> 
Sent by: "R-help" <r-help-bounces at r-project.org>
03/14/2019 08:43 PM

To
r-help at r-project.org, 
cc

Subject
[R] density vs. mass for discrete probability functions






Dear R users,

While experimenting with the dbinom() function and reading its
documentation (?dbinom) it reads that "dbinom gives the density" but
shouldn't it be called "mass" instead of "density"? I
assume that it
has something to do with keeping the function for "density" consistent
across discrete and continuous probability functions - but I am not
sure and was hoping someone could clarify?

Furthermore the help file for dbinom() function references a link
(http://www.herine.net/stat/software/dbinom.html) but it doesn't seem
to land where it should. Maybe this could be updated?

Thank you,
Stefan

______________________________________________
R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
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.


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