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Considering I have a collection of data. Let's say for example they are length 100. My hypothesis say that these data follow the alpha-stable distribution. Is there a way to calculate the alpha parameter of these data?

I would like to do that in python more specifically. All I found was that package http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.levy_stable.html#scipy.stats.levy_stable

which just calculates an alpha-stable distribution given the parameters of the distribution.

I am not that familiar with alpha-stable distributions. I will try to make it more clear using an example of Poisson distribution. If I have some data that I know they follow Poisson distribution isn't it possible to calculate the λ of that distribution? (Is this possible or am I miss something from statistics theory?)

Severin Pappadeux
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luthien
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If I have some data that I know they follow Poisson distribution isn't it possible to calculate the λ of that distribution? (Is this possible or am I miss something from statistics theory?)

Sure. Mean of Poisson is equal to λ, so compute mean of your data and try ti use it. Because variance is equal to λ as well, there is quick check how Poisson your data are - compute variance as well and compare to mean/λ. If they are comparable, you're on a good track, though some MC sampling at the end might help as well.

Wrt alpha-stable distribution, I would start with computing data skewness, mean, median and mode. If data has no/little skew and mean, median and mode close, then one can assume that beta is 0 and mu is known. You have only two parameters left to define (alpha and c), and building PDF as FT and fitting might work

Severin Pappadeux
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  • thank you for your info on Poisson distribution. Now I understand it better. I found the answer to my question using a module i found here http://www.logarithmic.net/pfh/pylevy – luthien Aug 03 '16 at 16:09