The purpose of this dissertation was to empirically investigate the Type I error and power rates of four data transformations that produce a variety of non-normal distributions. Specifically, the transformations investigated were (a) the g-and-h, (b) the generalized lambda distribution (GLD), (c) the power method, and (d) the Burr families of distributions in the context of between-subjects and within-subjects analysis of variance (ANOVA). The traditional parametric F tests and their nonparametric counterparts, the Kruskal-Wallis (KW) and Friedman (FR) tests, were selected to be used in this investigation. The four data transformations produce non-normal distributions that have either valid or invalid probability density functions (PDFs). Specifically, the data generating procedures will produce distributions with valid PDFs if and only if the transformations are strictly increasing - otherwise the distributions are considered to be associated with invalid PDFs. As such, the primary objective of this study was to isolate and investigate the behaviors of the four data transformation procedures themselves while holding all other conditions constant (i.e., sample sizes, effect sizes, correlation levels, skew, kurtosis, random seed numbers, etc. all remain the same). The overall results of the Monte Carlo study generally suggest that when the distributions have valid probability density functions (PDFs) that the Type I error and power rates for the parametric (or nonparametric) tests were similar across all four data transformations. It is noted that there were some dissimilar results when the distributions were very skewed and near their associated boundary conditions for a valid PDF. These dissimilarities were most pronounced in the context of the KW and FR tests. In contrast, when the four transformations produced distributions with invalid PDFs, the Type I error and power rates were more frequently dissimilar for both the parametric F and nonparametric (KW, FR) tests. The dissimilarities were most pronounced when the distributions were skewed and heavy-tailed. For example, in the context of a parametric between subjects design, four groups of data were generated with (a) sample sizes of 10, (b) standardized effect size of 0.50 between groups, (c) skew of 2.5 and kurtosis of 60, (d) power method transformations generating distributions with invalid PDFs, and (e) g-and-h and GLD transformations both generating distributions with valid PDFs. The power results associated with the power method transformation showed that the F-test (KW test) was rejecting at a rate of .32 (.86). On the other hand, the power results associated with both the g-and-h and GLD transformations showed that the F-test (KW test) was rejecting at a rate of approximately .19 (.26). The primary recommendation of this study is that researchers conducting Monte Carlo studies in the context described herein should use data transformation procedures that produce valid PDFs. This recommendation is important to the extent that researchers using transformations that produce invalid PDFs increase the likelihood of limiting their study to the data generating procedure being used i.e. Type I error and power results may be substantially disparate between different procedures. Further, it also recommended that g-and-h, GLD, Burr, and fifth-order power method transformations be used if it is desired to generate distributions with extreme skew and/or heavy-tails whereas third-order polynomials should be avoided in this context.

The main focus of this thesis is to develop full parametric and semiparametric Bayesian inference for data arising from triangular distributions. A natural consequence of working with such distributions is it allows one to consider regression models where the response variable is now the mode of the data distribution. A new family of nonparametric prior distributions is developed for a certain class of convex densities of particular relevance to mode regressions. Triangular distributions arise in several contexts such as geosciences, econometrics, finance, health care management, sociology, reliability engineering, decision and risk analysis, etc. In many fields, experts, typically, have a reasonable idea about the range and most likely values that define a data distribution. Eliciting these quantities is thus, generally, easier than eliciting moments of other commonly known distributions. Using simulated and actual data, applications of triangular distributions, with and without mode regressions, in some of the aforementioned areas are tackled. / text

This investigation is designed to find the net rate of decrease in the component of velocity parallel to the original direction of motion of a proton moving through an electron gas exhibiting a non-spherical velocity distribution.

This paper discusses results of a computer simulation to investigate several different tests when sampling several distributions. The hypothesis H0: μ=0 was tested against H0: μ≠0, using the usual t-test, trimmed t-test, the Jackkinfe, the Boostrap and signed-rank test. The p-values and empirical power show that the Bootstrap is as good as the t-test. The Jackknife procedure is too liberal, always obtaining small p-values. The signed-rank is a fairly good test if the data follows the Cauchy Distribution.

The LHC, with its center-of-mass energy of 7 TeV, offers the chance to investigate the fundamental constituents of matter at a higher energy scale than ever before. Using the data acquired by the ATLAS detector in the summer of 2010, two different measures of the angular distributions of dijet final states are studied and compared to Standard Model QCD expectations. Such a comparison is used to set new stringent limits on the existence of quark substructure.

The LHC, with its center-of-mass energy of 7 TeV, offers the chance to investigate the fundamental constituents of matter at a higher energy scale than ever before. Using the data acquired by the ATLAS detector in the summer of 2010, two different measures of the angular distributions of dijet final states are studied and compared to Standard Model QCD expectations. Such a comparison is used to set new stringent limits on the existence of quark substructure.

No description available.

We use inequalities to design short universal algorithms that can be used to generate random variates from large classes of univariate continuous or discrete distributions (including all log-concave distributions). The expected time is uniformly bounded over all these distributions. The algorithms can be implemented in a few lines of high level language code. In opposition to other black-box algorithms hardly any setup step is required and thus it is superior in the changing parameter case. (author's abstract) / Series: Preprint Series / Department of Applied Statistics and Data Processing

Infinitely divisible distributions and processes have been the object of extensive research not only from the theoretical point of view but also for practical use, for example, in queueing theory or mathematical finance. In this thesis, we will study some of their subclasses with a view towards financial modeling. As generalizations of stable distributions, we study the tempered stable distributions and introduce the new classes of layered stable distributions as well as the mixed stable distributions, along with the corresponding Levy processes. As a further generalization of infinitely divisible processes, fractional tempered stable motions are defined. These theoretical studies will be complemented by some more practical ones, such as the simulation of sample paths, parameter estimations, financial portfolio hedging, and solving stochastic differential equations.

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