Probability Commons^™

Supervised Classification Using Copula And Mixture Copula, Sumen Sen

Mathematics & Statistics Theses & Dissertations

Statistical classification is a field of study that has developed significantly after 1960's. This research has a vast area of applications. For example, pattern recognition has been proposed for automatic character recognition, medical diagnostic and most recently in data mining. Classical discrimination rule assumes normality. However in many situations, this assumption is often questionable. In fact for some data, the pattern vector is a mixture of discrete and continuous random variables. In this dissertation, we use copula densities to model class conditional distributions. Such types of densities are useful when the marginal densities of a pattern vector are not normally …

Mathematical Models Of Games Of Chance: Epistemological Taxonomy And Potential In Problem-Gambling Research, Catalin Barboianu

UNLV Gaming Research & Review Journal

Games of chance are developed in their physical consumer-ready form on the basis of mathematical models, which stand as the premises of their existence and represent their physical processes. There is a prevalence of statistical and probabilistic models in the interest of all parties involved in the study of gambling – researchers, game producers and operators, and players – while functional models are of interest more to math-inclined players than problem-gambling researchers. In this paper I present a structural analysis of the knowledge attached to mathematical models of games of chance and the act of mathematical modeling, arguing that such …

The Relationship Between Self-Determination And Client Outcomes Among The Homeless, Samuel M. Hanna

Electronic Theses, Projects, and Dissertations

This paper has attempted to determine if there is a significant relationship between self-determination and client outcomes among the homeless. The study has been based upon the conceptual framework set forth in Self-Determination Theory. The purpose of the study was to explore the relationship between self-determination and client outcomes among the homeless. Using a data collection instrument, based on empirically validated instrumentation, clients from several homeless service providers in the City of San Bernardino were assessed for the level of self-determination and autonomy support they experience within these agencies. Outcome measures included such things as whether the client was going …

Video Event Understanding With Pattern Theory, Fillipe Souza, Sudeep Sarkar, Anuj Srivastava, Jingyong Su

MODVIS Workshop

We propose a combinatorial approach built on Grenander’s pattern theory to generate semantic interpretations of video events of human activities. The basic units of representations, termed generators, are linked with each other using pairwise connections, termed bonds, that satisfy predefined relations. Different generators are specified for different levels, from (image) features at the bottom level to (human) actions at the highest, providing a rich representation of items in a scene. The resulting configurations of connected generators provide scene interpretations; the inference goal is to parse given video data and generate high-probability configurations. The probabilistic structures are imposed using energies that …

Using Capture-Mark-Recapture Techniques To Estimate Detection Probabilities & Fidelity Of Expression For The Critically Endangered James Spinymussel (Pleurobema Collina)., Alaina C. Esposito

Masters Theses, 2010-2019

The critically endangered James Spinymussel (Pleurobema collina) is a species of freshwater mussel endemic to Virginia’s James and Dan River basins. In the last 20 years, P. collina has experienced a substantial decline in numbers and currently occupies approximately 10% of its original habitat; however, little information is known about this species to assist in conservation. A 230-meter reach of transitional habitat in Swift Run was selected for repeat observations to estimate detection probabilities using a Capture-Mark-Recapture framework. In June 2014, visual scouting began to locate and tag P. collina (including other mussels in the community) with PIT …

No-Arbitrage Option Pricing And The Binomial Asset Pricing Model, Nicholas S. Hurley

Honors College Theses

Financial markets often employ the use of securities, which are defined to be any kind of tradable financial asset. Common types of securities include stocks and bonds. A particular type of security, known as a derivative security (or simply, a derivative), are financial instruments whose value is derived from another underlying security or asset (such as a stock). A common kind of derivative is an option, which is a contract that gives the holder the right but not the obligation to go through with the terms of said contract. An example of an option is the European Option, which we …

Boundary Problems For One And Two Dimensional Random Walks, Miky Wright

Masters Theses & Specialist Projects

This thesis provides a study of various boundary problems for one and two dimensional random walks. We first consider a one-dimensional random walk that starts at integer-valued height k > 0, with a lower boundary being the x-axis, and on each step moving downward with probability q being greater than or equal to the probability of going upward p. We derive the variance and the standard deviation of the number of steps T needed for the height to reach 0 from k, by first deriving the moment generating function of T. We then study two types of two-dimensional random walks with …

Exact Statistical Inferences For Functions Of Parameters Of The Log-Gamma Distribution, Joseph F. Mcdonald

UNLV Theses, Dissertations, Professional Papers, and Capstones

The log-gamma model has been used extensively for flood frequency analysis and is an important distribution in reliability, medical and other areas of lifetime testing. Conventional methods fails to provide exact solutions for the log-gamma model while asymptotic methods provide approximate solutions that often have poor performance for typical sample sizes. The two parameter log-gamma distribution is examined using the generalized p-value approach. The methods are exact in the sense that the tests and the confidence intervals are based on exact probability statements rather than on asymptotic approximations. Exact tests and exact confidence intervals for the parameter of interest based …

Modeling Traffic At An Intersection, Kaleigh L. Mulkey, Saniita K. Fasenntao

Symposium of Student Scholars

The main purpose of this project is to build a mathematical model for traffic at a busy intersection. We use elements of Queueing Theory to build our model: the vehicles driving into the intersection are the “arrival process” and the stop light in the intersection is the “server.”

We collected traffic data on the number of vehicles arriving to the intersection, the duration of green and red lights, and the number of vehicles going through the intersection during a green light. We built a SAS macro code to simulate traffic based on parameters derived from the data.

In our program …

Bootstrapping Vs. Asymptotic Theory In Property And Casualty Loss Reserving, Andrew J. Difronzo Jr.

Honors Projects in Mathematics

One of the key functions of a property and casualty (P&C) insurance company is loss reserving, which calculates how much money the company should retain in order to pay out future claims. Most P&C insurance companies use non-stochastic (non-random) methods to estimate these future liabilities. However, future loss data can also be projected using generalized linear models (GLMs) and stochastic simulation. Two simulation methods that will be the focus of this project are: bootstrapping methodology, which resamples the original loss data (creating pseudo-data in the process) and fits the GLM parameters based on the new data to estimate the sampling …

Defeatism Defeated, Max Baker-Hytch, Matthew A. Benton

SPU Works

Many epistemologists are enamored with a defeat condition on knowledge. In this paper we present some implementation problems for defeatism, understood along either internalist or externalist lines. We then propose that one who accepts a knowledge norm of belief, according to which one ought to believe only what one knows, can explain away much of the motivation for defeatism. This is an important result, because on the one hand it respects the plausibility of the intuitions about defeat shared by many in epistemology; but on the other hand, it obviates the need to provide a unified account of defeat which …

The Simulation & Evaluation Of Surge Hazard Using A Response Surface Method In The New York Bight, Michael H. Bredesen

UNF Graduate Theses and Dissertations

Atmospheric features, such as tropical cyclones, act as a driving mechanism for many of the major hazards affecting coastal areas around the world. Accurate and efficient quantification of tropical cyclone surge hazard is essential to the development of resilient coastal communities, particularly given continued sea level trend concerns. Recent major tropical cyclones that have impacted the northeastern portion of the United States have resulted in devastating flooding in New York City, the most densely populated city in the US. As a part of national effort to re-evaluate coastal inundation hazards, the Federal Emergency Management Agency used the Joint Probability Method …

Security Analysis On Network Systems Based On Some Stochastic Models, Xiaohu Li

LSU New Orleans Theses and Dissertations

Due to great effort from mathematicians, physicists and computer scientists, network science has attained rapid development during the past decades. However, because of the complexity, most researches in this area are conducted only based upon experiments and simulations, it is critical to do research based on theoretical results so as to gain more insight on how the structure of a network affects the security. This dissertation introduces some stochastic and statistical models on certain networks and uses a k-out-of-n tolerant structure to characterize both logically and physically the behavior of nodes. Based upon these models, we draw several illuminating results …

Choosing Between Parametric And Non-Parametric Tests, Russ Johnson

Journal of Undergraduate Research at Minnesota State University, Mankato

A common question in comparing two sets of measurements is whether to use a parametric testing procedure or a non-parametric procedure. The question is even more important in dealing with smaller samples. Here, using simulation, several parametric and nonparametric tests, such as, t-test, Normal test, Wilcoxon Rank Sum test, van-der Waerden Score test, and Exponential Score test are compared.

Comparison Of Hazard, Odds And Risk Ratio In The Two-Sample Survival Problem, Benedict P. Dormitorio

Dissertations

Cox proportional hazards is the standard method for analyzing treatment efficacy when time-to-event data is available. In the absence of time-to-event, investigators may use logistic regression which only requires relative frequencies of events, or Poisson regression which requires only interval-summarized frequency tables of time-to-event. When event frequencies are used instead of time-to-events, does it always result in a loss in power?

We investigate the relative performance of the three methods. In particular, we compare the power of tests based on the respective effect-size estimates (1)hazard ratio (HR), (2)odds ratio (OR), and (3)risk ratio (RR). We use a variety of survival …

Some New Probability Distributions Based On Random Extrema And Permutation Patterns, Jie Hao

Electronic Theses and Dissertations

In this paper, we study a new family of random variables, that arise as the distribution of extrema of a random number N of independent and identically distributed random variables X₁,X₂, ..., X_N, where each X_i has a common continuous distribution with support on [0,1]. The general scheme is first outlined, and SUG and CSUG models are introduced in detail where X_i is distributed as U[0,1]. Some features of the proposed distributions can be studied via its mean, variance, moments and moment-generating function. Moreover, we make some other choices for …

Asymmetric Empirical Similarity, Joshua C. Teitelbaum

Georgetown Law Faculty Publications and Other Works

The paper offers a formal model of analogical legal reasoning and takes the model to data. Under the model, the outcome of a new case is a weighted average of the outcomes of prior cases. The weights capture precedential influence and depend on fact similarity (distance in fact space) and precedential authority (position in the judicial hierarchy). The empirical analysis suggests that the model is a plausible model for the time series of U.S. maritime salvage cases. Moreover, the results evince that prior cases decided by inferior courts have less influence than prior cases decided by superior courts.

Meta-Analysis Of Social-Personality Psychological Research, Blair T. Johnson, Alice H. Eagly

CHIP Documents

This publication provides a contemporary treatment of the subject of meta-analysis in relation to social-personality psychology. Meta-analysis literally refers to the statistical pooling of the results of independent studies on a given subject, although in practice it refers as well to other steps of research synthesis, including defining the question under investigation, gathering all available research reports, coding of information about the studies and their effects, and interpretation/dissemination of results. Discussed as well are the hallmarks of high-quality meta-analyses.

Toward A Morphometric Phylogeny Of Caddo Ceramics: A Test Of 3d Geometric Morphometrics, Robert Z. Selden Jr., Timothy K. Perttula, Michael J. O'Brien

CRHR: Archaeology

In this poster we use 3D geometric morphometrics as an exploratory tool for examining diversity in vessel form (or shape) among 27 whole or reconstructed Caddo vessels from the Vanderpool site in Smith County, Texas. Forty-one landmarks from each vessel were exported to version 2.5 of Morphologika for generalized Procrustes analysis and principal components analysis and were then exported to R for cluster analysis (depending on sample size). Despite the small sample size, results indicate that 3D geometric morphometric analysis is an avenue of ceramic research where substantive analytical gains can be realized.

Cycle Lengths Of Θ-Biased Random Permutations, Tongjia Shi

HMC Senior Theses

Consider a probability distribution on the permutations of n elements. If the probability of each permutation is proportional to θ^K, where K is the number of cycles in the permutation, then we say that the distribution generates a θ-biased random permutation. A random permutation is a special θ-biased random permutation with θ = 1. The m^th moment of the r^th longest cycle of a random permutation is Θ(n^m), regardless of r and θ. The joint moments are derived, and it is shown that the longest cycles of a permutation can either be positively or …