Generating integer random numbers from power-law distribution

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Sunstar
Sunstar 2013-12-13
回答： Weijia Chen 2019-9-18
Is there a code to generate integer random numbers through power-law distribution of the form p(x)=x^-(alpha+1)?
thanks in advance

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Image Analyst
Image Analyst 2013-12-13
Try this: RANDRAW

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Miguel Ángel
Miguel Ángel 2013-12-13
编辑：Miguel Ángel 2013-12-13
I don't know if round,ceil or floor is correct, but in case this may be a way
n=1000;
p=rand(1,n);
alpha=0.1;
%inverse of distribution
%properties of logs %LOGa(n) = LOGb(N) / LOGb(a)
%~round/ceil/floor
x=round(log(p)/log(alpha+1));
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Sunstar
Sunstar 2013-12-13
Thank you for your reply. Unfortunately, I cannot simply round or floor or ceil. I need to generate real integers.

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Roger Stafford
Roger Stafford 2013-12-13
The distribution you mention is equivalent to the zeta distribution with alpha+1 replaced by s. See the website
http://en.wikipedia.org/wiki/Zeta_distribution
As Image Analyst has mentioned, there is a File Exchange contribution called 'randraw' which is located at:
http://www.mathworks.com/matlabcentral/fileexchange/7309-randraw
which claims to generate random numbers in accordance with fifty various distributions including the zeta distribution. It might be what you need.
Weijia Chen
Weijia Chen 2019-9-18
I also meet the same problem. The minimum integer that zeta distribution can generate seems to be 1, but I hope 0 can be generated. Is there any other distributin can do this? Thank you

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