Timeline for When can you describe a population and its component subpopulations with the same parametric family of distributions?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 15, 2023 at 16:06 | history | edited | Glorfindel | CC BY-SA 4.0 |
2 broken links fixed, cf. https://meta.mathoverflow.net/q/5301/70594
|
| May 6, 2016 at 21:13 | vote | accept | andrewH | ||
| Sep 28, 2012 at 21:44 | comment | added | andrewH | Hi an12! Thanks for your comment. Yes, you are absolutely correct: I am not talking about samples from a single population, but about a larger population that is divided into disjoint sub-populations with different parameters. I called this a merger, but knowing that I should call it a mixture is very helpful in finding the literature. | |
| Sep 23, 2012 at 9:08 | history | edited | an12 | CC BY-SA 3.0 |
added 476 characters in body
|
| Sep 23, 2012 at 8:56 | comment | added | an12 | Hi Andrew. Could you reformulate the question more mathematically? According to your comment, this is a different problem from the consistency under sampling one. If you have say $p$ different sub-population, each distributed according to the same parametric family, but possibly with different parameter, then the distribution of the population is a mixture. So, if that is your question, it becomes then which distributions are closed under mixing. | |
| Sep 23, 2012 at 8:04 | comment | added | andrewH | This is a very interesting paper. Thank you so much for bringing it to my attention. But I think my question differs. I am not asking whether, e.g., the parameters of the PDF of income in a state can be used to represent those of the nation, as an estimator. Nor am I asking whether the parameters of the nation can be decomposed into a function of the parameters of the states' distributions. Instead, I am asking whether there are parametric families s.t., if all the state PDFs are drawn from that family with varying parameters, the national PDF will be from the same family for some parameters. | |
| Sep 23, 2012 at 5:30 | history | answered | an12 | CC BY-SA 3.0 |