[R] density vs. mass for discrete probability functions

[peter dalgaard]

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 using 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
> 
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-- 
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
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