Is there a central limit theorem for power laws?
Power laws can be found in various fields including physics, where its emergence is frequently associated with critical phenomena. Why is the power law so common? Perhaps like the normal distribution, the power law distribution also has its own central limit. In this FYP, we first verify the cent...
محفوظ في:
| المؤلف الرئيسي: | |
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| مؤلفون آخرون: | |
| التنسيق: | Final Year Project |
| اللغة: | English |
| منشور في: |
Nanyang Technological University
2024
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| الموضوعات: | |
| الوصول للمادة أونلاين: | https://hdl.handle.net/10356/175709 |
| الوسوم: |
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| الملخص: | Power laws can be found in various fields including physics, where its emergence is
frequently associated with critical phenomena. Why is the power law so common? Perhaps
like the normal distribution, the power law distribution also has its own central limit. In this
FYP, we first verify the central limit theorem and the generalized central limit theorem for
stable distributions through numerical methods. We then investigate the sum of power law
random variables by sampling from the Pareto distribution and analyzing how the tail exponent
of the resulting sum of power laws is affected. We also investigate the convergence of the
sum of power laws to the alpha-stable distribution and for which values of α it converges to.
Methods of generating power laws are also examined, along with the conditions when it stops
generating power laws. We first start by using the uniform distribution to sample values as the
parameter of an exponential distribution and investigate the resulting power law by varying
the interval of values the uniform distribution can take. We then investigate another method
using sums of lognormal random variables, where the number of random variables summed
is determined by a binomial random variable and vary σ of the lognormal random variable to
control the power law tail of the resulting distribution |
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