Timeline for What are we modelling when a gamma distribution has non-integer shape parameter
Current License: CC BY-SA 4.0
11 events
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| Nov 29, 2022 at 12:53 | comment | added | Nick Cox | I like it when distributions arise from plausible models, but many have no clear motivation and some have so many that you are hard pushed to know which to believe. There are all sorts of ways, for example, to get negative binomials, or the same rose under different names. | |
| Nov 29, 2022 at 12:43 | comment | added | Cai | @NickCox - The fact that it has a general shape is fine, however I am talking specifically about deriving the distribution based on a specific situation. Sure, it may have a general shape, but that property is not an explanation as to where it came from in the first place, nor is it an explanation as to what specifically is being modelled theoretically when we have an non-integer (+ve) shape parameter. This is the part I find very frustrating, is that I can only find derivations for an integer shape parameter, which leaves an infinite number of cases unexplained. Hence my question. | |
| Nov 29, 2022 at 0:35 | history | became hot network question | |||
| Nov 29, 2022 at 0:00 | history | tweeted | twitter.com/StackStats/status/1597379892357865472 | ||
| Nov 28, 2022 at 17:09 | comment | added | whuber♦ | Chi-squared variables with odd d.f. have Gamma distributions with non-integral shape parameters. If you want a mathematical derivation, look into Jacobi sums on arbitrary fields or contemplate the classical relationship between Gamma and the cosecant function. | |
| Nov 28, 2022 at 17:07 | comment | added | Avraham | You also may want to see the second answer here: mathoverflow.net/q/38821/39144 | |
| Nov 28, 2022 at 16:44 | comment | added | Nick Cox | Fact is the gamma distribution is a fairly general shape and its interpretations as a sum of exponentials, or as the composite result of events in time, only cover special cases. It's up to you whether you find that ridiculous. | |
| Nov 28, 2022 at 16:44 | answer | added | Roger V. | timeline score: 6 | |
| Nov 28, 2022 at 16:39 | history | edited | Roger V. | CC BY-SA 4.0 |
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| S Nov 28, 2022 at 16:31 | review | First questions | |||
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| S Nov 28, 2022 at 16:31 | history | asked | Cai | CC BY-SA 4.0 |