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
density vs. mass for discrete probability functions
7 messages · Stefan Schreiber, Peter Dalgaard, Spencer Graves +2 more
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
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.
Hello, Yes, there is even an old discussion on this on r-devel, dated August, 10 2013. See [1]. [1] https://r-project.markmail.org/search/?q=broken-link-in-docs-for-Binormial-functions#query:broken-link-in-docs-for-Binormial-functions+page:1+mid:rf6tbiokcdyai6el+state:results Hope this helps, Rui Barradas ?s 14:21 de 15/03/2019, Stefan Schreiber escreveu:
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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______________________________________________ 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.