# Viewing PMF as an instance of a PDF

I'm having difficulties in thinking about the probability mass function (PMF) as a special case of the probability density function (PDF).

I understand that PMF's are used in discrete examples, but in the extreme, we could have a continuous distribution with small clusters or neighbourhoods around $$\mathbb{Z}$$ (to simulate the concentrated mass in a point in the discrete case) of infinite density.

Is the modelling of infinite density correct? Or should it be $$0$$ instead? Am I missing anything or doing anything wrong?

If you happen to have suggestions of viewing this problem in other ways, do suggest them.

• Could you describe the actual problem that you are facing? What exactly do you want to model and how? What is the problem? – Tim Jan 29 at 14:50
• @StubbornAtom your link seems to point to a linear algebra question that has nothing to do with this Q – Juho Kokkala Jan 31 at 18:12
• @JuhoKokkala Dear god! I meant this one: math.stackexchange.com/questions/3095012/…. – StubbornAtom Jan 31 at 19:09
• I'm voting to close this question as off-topic because it has been asked by the OP on math.SE as well (math.stackexchange.com/q/3095012/15941) where it has been answered already. – Dilip Sarwate Feb 3 at 14:22