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| 9 Jul 2024 |
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| andtorg | hi, would anyone be so kind to recommend a book or other resources on power law, pareto distribution, zipf law et similia? TIA | 07:51:16 |
 Christoph | @andtorg:matrix.org: Are you looking for something specific? A mathematical treatise? Applications? Maybe this one is useful, or the references therein:
https://arxiv.org/abs/cond-mat/0412004 | 10:04:58 |
| andtorg | In reply to @hpotsirhc:matrix.org
@andtorg:matrix.org: Are you looking for something specific? A mathematical treatise? Applications? Maybe this one is useful, or the references therein:
https://arxiv.org/abs/cond-mat/0412004 many thanks, I already read it.. to tell better I'm still struggling on it; I got the idea but the math is slightly above my current level. I also read some papers/articles by B. Mandelbrot and N.N. Taleb. Basically I'm trying to understand if some data i have collected for a job i'm running as a consultant can be modeled as a power law in order to take some decisions; so I would say I have an interest in theory but with an application in mind | 10:12:44 |
| Christoph | Did you plot your data in a log-log-plot already? Does it make a straight line? | 10:17:53 |
| andtorg | yes, the dataset suggest a power law. On a log scale i got a fairly clear -1.9 alpha, as confirmed by the analytical formula stated in the article you quoted. I feel I need a deeper knowledge of the model in order to understand if it is correct to say that this specific process would have that power law behaviour also in the future | 10:27:06 |
| 10 Jul 2024 |
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| Christoph | @andtorg:matrix.org: In https://www.stat.berkeley.edu/~aldous/Research/Ugrad/Willy_Lai.pdf, the author uses the Kolmogorov-Smirnov-Test as a criterion to determine if the power law is a good fit for.the data in question. With the same method, they decide that some other but similarly looking distributions do not fit the data.
For my feeling, this procedue is easy to critique. What if the correct distribution just isn't in the set of distributions you try? Why did they choose 10% as a p-value? And p-values are a whole topic themselves! But you sure can try this to get a better familiarity with the data.
I'd prefer a model for the data that motivates that the power law is the correct distribution, though.
In Random Graphs and Complex Networks https://www.win.tue.nl/~rhofstad/NotesRGCN.pdf chapter 1.7.3 discusses estimation of the exponent of a power law, which is easy to get wrong, and it advertises two references towards the end.
There is discussion of power laws all over the book, and there are models that lead to/explain power laws, like preferential attachment (and even measurement biases that can accidentially introduce the power law during data collection). The author has recently completed a second book on random graphs https://www.win.tue.nl/~rhofstad/NotesRGCNII.pdf which might contain more details and more recent developments, but I didn't read it yet. | 20:11:52 |
| 11 Jul 2024 |
| andtorg | wow, really big thanks. I'll try and look through the resources you provided. I'm also planning to read again some chapters from "The misbehavior of markets" by B. Mandelbrot, R.L. Hudson: though divulgative, as far as i remember it contains several discussions about power laws hidden everywhere. | 07:49:48 |
| 12 Jul 2024 |
 itozylu | Hello, could someone perhaps help me with this problem? Long story short, I have to write about enzyme kinetics because my tutor has got it in his head but with a statistical approach and I am not finding much theory about it.
I have already talked about the michaelis-menten equation, possible linearizations and multivariate linear regression models. I also refer to generalized linear and additive models (GAM and GLM) and I was thinking of putting something from Akaike but I can't find much else on the subject interesting or that I can put. Any thoughts on this that might clarify something for me or that I should add? | 07:32:24 |
 Justin | If you want something challenging, look into transporter kinetics. | 11:53:01 |
| Justin | * itozylu: If you want something challenging, look into transporter kinetics. | 11:53:37 |
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