[R] density vs. mass for discrete probability functions

[Spencer Graves]

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
>
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