1

My research topic is about theory of distribution—studying probability distributions and their properties—which was suggested to me by my adviser. This is not my research area of interest, but I'll do it anyway, forcefully. I've searched through the internet, but I'm still confused about the difference between the class and the family of probability distributions.

What it says from: Family vs. class of distributions - definitions

"class - any collection of distributions; family - an indexed collection of distributions."

What does it mean by "indexed" in the context? (Sorry for poor understanding.)

From what I understood, it means that: class is just a member of a family (which is the group I suppose), doesn't it?

Are there formal definitions for the distinction between the two? Any textbook recommendations for a starter that talks about probability distribution—theory, models, methods, inference, applications?

Thank you!

Adameve
  • 11
  • 2
  • 2
    These are informal definitions: an exponential family of distributions is sometimes called an exponential class of distributions (to add to the confusion, the set of exponential distributions is an example of an exponential family of distributions but there are many other exponential families). I am not sure "indexed" is the best word here and "parametrised" might be better: the set of exponential distributions is often parametrised by a rate or scale parameter. – Henry Mar 24 '24 at 20:35
  • @adameve in the body text you are asking more specific about the meaning of 'indexed' but the title makes it just a duplicate of the question that you link to. Could you be more specific and clear about the difference with the other question. – Sextus Empiricus Mar 24 '24 at 20:41
  • Kendall's Advanced Theory of Statistics is a classic text https://books.google.com/books?id=3h1W1JCBvN0C&newbks=0&hl=en&source=newbks_fb Then there's Johnson and Kotz' four volumes on distributions -- discrete, continuous, univariate. – user78229 Mar 25 '24 at 13:35

0 Answers0