ESTIMATION, MODEL SELECTION, AND RESILIENCE OF POWER-LAW DISTRIBUTIONS

Wei, Yafei (2016) ESTIMATION, MODEL SELECTION, AND RESILIENCE OF POWER-LAW DISTRIBUTIONS. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Abstract

This thesis includes a series studies on power-law distribution, which is a widely used distribution in vast areas such as biology, economy, social science and information science. There are three parts in the thesis.

The first part is parameter estimation of power-law distributions. We categorize variants of power-law distributions into six types. We proposed improvements on the estimation for some types, either decreasing bias or standard deviation of the estimates. We also proposed methods for some types if there is no corresponding estimation method yet.

The second part is model selection between non-truncated and truncated power-law distributions. We evaluated both criterion based methods and test based methods on the model selection, by calculating sensitivity and specificity of each method from simulation studies. We also proved some properties of the calculation to extend the result of the simulation study with a particular parameter setting to more general parameter settings.

The third part is exploring resilience of the power-law degree distribution of scale-free networks. We explored how the degree distribution changes if the network receives attacks to lose vertices and corresponding edges under random removal, normal curve removal and high degree removal strategies. We derived the form of expected degree distribution, which is not power law any more even one vertex is removed. We also conducted a simulation study by using goodness of fit test to see the validity of power law, which shows that power law is very resilient for random removal but fragile for high degree removal. We conducted simulation study to observe the change of parameters when the goodness of fit test shows that power law is a good fit.

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Details

Item Type:	University of Pittsburgh ETD
Status:	Unpublished
Creators/Authors:	Creators Email Pitt Username ORCID Wei, Yafei yaw24@pitt.edu YAW24
ETD Committee:	Title Member Email Address Pitt Username ORCID Committee Chair Iyengar, Satish ssi@pitt.edu SSI Committee Member Block, Henry hwb@pitt.edu HWB Committee Member Chen, Kehui khchen@pitt.edu KHCHEN Committee Member Wahed, Abdus S wahed@pitt.edu WAHED
Date:	15 June 2016
Date Type:	Publication
Defense Date:	9 December 2015
Approval Date:	15 June 2016
Submission Date:	12 April 2016
Access Restriction:	1 year -- Restrict access to University of Pittsburgh for a period of 1 year.
Number of Pages:	70
Institution:	University of Pittsburgh
Schools and Programs:	Dietrich School of Arts and Sciences > Statistics
Degree:	PhD - Doctor of Philosophy
Thesis Type:	Doctoral Dissertation
Refereed:	Yes
Uncontrolled Keywords:	power-law distribution, parameter estimation, bootstrap, starting point, model selection, truncated, resilience, degree distribution, scale-free network
Date Deposited:	15 Jun 2016 21:53
Last Modified:	15 Jun 2017 05:15
URI:	http://d-scholarship.pitt.edu/id/eprint/27667

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