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Is the term "probability distribution" mostly used as an "umbrella term" to indicate either a probability density function (PDF) or a probability mass function (PMF), or a cumulative distribution function (CDF), or a probability measure $\mu$, or other math objects?

Or it has a precise meaning and definition, allowing us to easily and clearly distinguish a "probability distribution" from either a probability density function (PDF) or from a probability mass function (PMF), or from a cumulative distribution function (CDF), or from a probability measure $\mu$, or other math objects?

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  • $\begingroup$ Hi @NuclearHoagie, thanks for the comment... I read that question and your answer there... about your first paragraph A probability distribution is just about anything that defines the likelihood of certain outcomes from an experiment. That can be defined in different ways, including the probability density function (PDF) for continuous variables, or the probability mass function (PMF) .... you wrote that a "probability distribution" can be "defined" in different ways, but my question is about the "usage" of that term... $\endgroup$
    – Ommo
    Commented Sep 7, 2023 at 16:06
  • $\begingroup$ From your answer I would infer a "Yes" as a reply to my question, i.e. Yes, the term "probability distribution" is mostly used as an "umbrella term" to indicate either a probability density function (PDF) or a probability mass function (PMF), or a cumulative distribution function (CDF), or a probability measure, or other math objects, but I would appreciate a confirmation of my guess.... Just a simple "Yes" would be good to me.... However, if you think it is basically the same question, ok, please go ahead to remove my question...even though, many people would have the same thought as I had.. $\endgroup$
    – Ommo
    Commented Sep 7, 2023 at 16:07
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    $\begingroup$ Yes, it's an umbrella term. A "probability distribution" in general describes the likelihood of different outcomes, but the representation of that behavior can take different forms with more specific names. $\endgroup$
    – Nuclear Hoagie
    Commented Sep 7, 2023 at 16:12
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    $\begingroup$ Yes, probability distribution is a broad name for... probability distributions, an assignment of probabilities to "outcomes." $\endgroup$
    – hardmath
    Commented Sep 7, 2023 at 16:12
  • $\begingroup$ Great, thanks a lot @NuclearHoagie!! That's clearer now :-) If you want to put it as an Answer, I will be happy to accept it! $\endgroup$
    – Ommo
    Commented Sep 7, 2023 at 16:13

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