# density vs. mass for discrete probability functions

7 messages
Open this post in threaded view
|

## 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 ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
Open this post in threaded view
|

## Re: density vs. mass for discrete probability functions

 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 > > ______________________________________________ > [hidden email] 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. ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
Open this post in threaded view
|

## Re: density vs. mass for discrete probability functions

Open this post in threaded view
|

## Re: density vs. mass for discrete probability functions

Open this post in threaded view
|

## Re: density vs. mass for discrete probability functions

 In reply to this post by Peter Dalgaard-2 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 <[hidden email]> 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 >> >> ______________________________________________ >> [hidden email] 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. ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
Open this post in threaded view
|

## Re: density vs. mass for discrete probability functions

 In reply to this post by Stefan Schreiber 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 <[hidden email]> Sent by: "R-help" <[hidden email]> 03/14/2019 08:43 PM To [hidden email], 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 ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.         [[alternative HTML version deleted]] ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
Open this post in threaded view
|