Date of Award

9-3-2019

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Department of Mathematics and Statistics

First Advisor

Christine M. Schubert Kabban, PhD

Abstract

This research centers on finding the statistical moments, network measures, and statistical tests that are most sensitive to various node degradations for the Barabási-Albert, Erdös-Rényi, and Watts-Strogratz network models. Thirty-five different graph structures were simulated for each of the random graph generation algorithms, and sensitivity analysis was undertaken on three different network measures: degree, betweenness, and closeness. In an effort to find the statistical moments that are the most sensitive to degradation within each network, four traditional moments: mean, variance, skewness, and kurtosis as well as three non-traditional moments: L-variance, L-skewness, and L-kurtosis were examined. Each of these moments were examined across 18 degrade settings to highlight which moments were able to detect node degradation the quickest. Closeness and the mean were the most sensitive measures to node degradation across all scenarios. The results showed L-moments and L-moment ratios were less sensitive than traditional moments. Subsequently sample size guidance and confidence interval estimation for univariate and joint L-moments were derived across many common statistical distributions for future research with L-moments.

AFIT Designator

AFIT-ENC-DS-19-S-001

DTIC Accession Number

AD1084932

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