Reliable Statistical Methods and their Applications for Testing Incomplete Multidisciplinary Data
Date
2018
Authors
Guscott, Jake Callum
Editors
Advisors
Kizilersu, Ayse
Thomas, A. W.
Thomas, A. W.
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Thesis
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Abstract
Recently, left-truncated distributions have proved to be of use in modelling a range of phenomena in fields as diverse as finance, insurance, medicine, earthquake prediction and wind power. In this thesis, we present a comprehensive analysis of the left-truncated Weibull, loglogistic, lognormal and Pareto distributions in cases where the scale, shape or both parameters are unlmown and estimated from the data with the maximum likelihood estimator. We define criteria which ensure that the maximum likelihood equations have a unique solution. We determine the critical values of the Kolmogorov-Smirnov, Kuiper, Cramer-von Mises and Anderson-Darling goodness-of-fit tests when the parameters are unknown for all of the left-truncated distributions via quantile analysis. In this work, these critical values are coupled with a rigorous point estimation and uncertainty analysis, and compared to the critical values of the complete (untruncated) distributions in the literature. We find strong agreement between our results and the most recent additions to the literature. Analytically, we provide evidence that the critical values are parameter independent for all of the left-truncated distributions and goodness-of-fit tests. This result is verified by determining the critical values via Monte Carlo simulations for a range of parameter values. We find that the critical values are dependent upon sample size and truncation level (as percentage of the complete distribution), and determine suitable models to describe this behaviour. We modelled these critical values successfully for each of the three fitting scenarios (i) truncation level dependence, (ii) sample size dependence and (iii) truncation level and sample size dependence, which describes the behaviour for the critical values of all goodness-of-fit tests, left-truncated distributions and significance levels. The fact that one functional form describes the critical values for all different goodness-of-fit tests and distributions is a very useful and interesting result. The models are validated through an exhaustive power testing procedure, which also serves to compare the discriminatory power the four tests. We find the Anderson-Darling test has marginally better statistical power than the others in every situation and that the discrimantory power of all tests is weak for small sample sizes. We conclude the work by applying all these statistical methods to analysing the interarrival times of market orders on the London Stock Exchange for a range truncation values and sample sizes. We find that the left-truncated Weibull distribution most accurately describes this data and that increasing the truncation level significantly increases the pass rates.
School/Discipline
School of Physical Sciences
Dissertation Note
Thesis (MPhil) -- University of Adelaide, School of Physical Sciences, 2018
Provenance
This electronic version is made publicly available by the University of Adelaide in accordance with its open access policy for student theses. Copyright in this thesis remains with the author. This thesis may incorporate third party material which has been used by the author pursuant to Fair Dealing exceptions. If you are the owner of any included third party copyright material you wish to be removed from this electronic version, please complete the take down form located at: http://www.adelaide.edu.au/legals