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Some Contributions to Multivariate Non-Normality: Simulation, Computations and Missing Data Imputation
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Some Contributions to Multivariate Non-Normality: Simulation, Computations and Missing Data Imputation
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Dissertation
Some Contributions to Multivariate Non-Normality: Simulation, Computations and Missing Data Imputation
2020
Overview
We study and develop some simulation and missing data imputation methods for non-normal distributions. It mainly consists of three separate parts as follows.First, we introduce the R package KbMvtSkew to assess the univariate and multivariate skewness of a data set via the measure specified by Khattree and Bahuguna in 2018. Then we concentrate on certain nonnormal multivariate probability distributions and introduce the R package NonNorMvtDist. This package is used to generate random numbers from multivariate Lomax distribution which constitutes a very flexible family of skewed multivariate distributions. Further, by applying certain useful properties of multivariate Lomax distribution, multivariate cases of generalized Lomax, Mardia’s Pareto of Type I, Logistic, Burr, Cook-Johnson’s uniform, F and inverted beta can be also considered and random numbers from these distributions can be generated. The content of this package is then extended to the methods for the probability and the equicoordinate quantile calculations for all of these distributions.In the second part, we study a connection from Lomax to exponential distribution through the limiting distribution of a Lomax distribution scaled by its shape parameter. This fact well explains the strong similarity between Lomax and exponential distribution when the shape parameter of Lomax is large. We also explore the relationships between (generalized) Lomax and other distributions of exponential family such as Gamma, Beta type II and Rayleigh. Various properties of generalized double Pareto distribution are studied including representation of mixture of Student’s t and connection to Laplace (double exponential). We then conclude a hypothesis testing problem where these ideas are used and Khattree-Bahuguna’s skewness is used as a test statistic.The last part of our work is about imputation for non-normal multivariate continuous data. We develop multivariate Lomax-based EM imputation method and compare its performance with other normality-based approaches. Then, we introduce the multiple imputation approach based on Copula transformation, which is used to effectively transform multivariate non-normal data into normal. Through simulated and real non-normal multivariate datasets, we demonstrate that copula transformation significantly mitigates the impact of blind assumption of multivariate normal for non-normal multivariate data under the assumption that data are missing completely at random (MCAR).
Publisher
ProQuest Dissertations & Theses
Subject
ISBN
9798664725018
