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Feb 10, 2022 at 6:49 comment added Peiran Yu Thank you Bruce, this is helpful! And yea, I agree these thresholds like a minimum requirement for sample sizes should be a more meaningful discussion when a specific case provides context. I don't have that now. Just trying to understand at a high level, what are the common practices for determining population distribution.
Feb 8, 2022 at 3:04 vote accept Peiran Yu
Feb 4, 2022 at 4:34 comment added BruceET As it seems you may have guessed (4) and (5) often go together. Software in (4) tries out it's guesses using (5) and to some extent discards bad guesses. In (4) large samples tend to work better, but I don't recall ever running into a minimum requirement. If sample is huge (5) may reject a useful dist'n because of a quirk in the sample that's of little practical importance. Some GOF tests won't accept sample sizes over 5000. // If you have specific applications in mind as per @kjetil 's comment, please mention details that might get addl useful answers.
Feb 4, 2022 at 4:01 comment added Peiran Yu Thank you for the very detailed and valuable answer! It is true that in many situations like the studies of physics, the distribution types are set. I appreciate the sharing of the (4) Distribution-finding software procedures & (5) Goodness of fit tests too. On that, I wonder what's the main difference, in terms of applicabilities, between these two? When do we use (4), and when do we use (5)? For example, in (4) you said we need to have "large samples", is there a required size for these "large samples"? Maybe more than a few thousands?
Feb 4, 2022 at 3:16 vote accept Peiran Yu
Feb 4, 2022 at 3:22
Feb 4, 2022 at 2:45 history edited BruceET CC BY-SA 4.0
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Feb 4, 2022 at 2:39 history edited BruceET CC BY-SA 4.0
added 200 characters in body
Feb 4, 2022 at 2:20 history answered BruceET CC BY-SA 4.0