Probability Commons^™

Gilmore Girls And Instagram: A Statistical Look At The Popularity Of The Television Show Through The Lens Of An Instagram Page, Brittany Simmons

Student Scholar Symposium Abstracts and Posters

After going on the Warner Brothers Tour in December of 2015, I created a Gilmore Girls Instagram account. This account, which started off as a way for me to create edits of the show and post my photos from the tour turned into something bigger than I ever could have imagined. In just over a year I have over 55,000 followers. I post content including revival news, merchandise, and edits of the show that have been featured in Entertainment Weekly, Bustle, E! News, People Magazine, Yahoo News, & GilmoreNews.

I created a dataset of qualitative and quantitative outcomes from my …

Inference On The Stress-Strength Model From Weibull Gamma Distribution, Mahmoud Mansour, Rashad El-Sagheer, M. A. W. Mahmoud Prof.

Basic Science Engineering

No abstract provided.

The Battle Against Malaria: A Teachable Moment, Randy K. Schwartz

Journal of Humanistic Mathematics

Malaria has been humanity’s worst public health problem throughout recorded history. Mathematical methods are needed to understand which factors are relevant to the disease and to develop counter-measures against it. This article and the accompanying exercises provide examples of those methods for use in lower- or upper-level courses dealing with probability, statistics, or population modeling. These can be used to illustrate such concepts as correlation, causation, conditional probability, and independence. The article explains how the apparent link between sickle cell trait and resistance to malaria was first verified in Uganda using the chi-squared probability distribution. It goes on to explain …

The Conditional Poisson Process And The Erlang And Negative Binomial Distributions, Anurag Agarwal, Peter Bajorski, David L. Farnsworth, James E. Marengo, Wei Qian

Articles

It is a well known fact that for the hierarchical model of a Poisson random variable Y whose mean has an Erlang distribution, the unconditional distribution of Y is negative binomial. However, the proofs in the literature provide no intuitive understanding as to why this result should be true. It is the purpose of this manuscript to give a new proof of this result which provides such an understanding. The memoryless property of the exponential distribution allows one to conclude that the events in two independent Poisson processes may be regarded as Bernoulli trials, and this fact is used to …

Quantifying Similarity In Reliability Surfaces Using The Probability Of Agreement, Nathaniel Stevens, C. M. Anderson-Cook

Mathematics

When separate populations exhibit similar reliability as a function of multiple explanatory variables, combining them into a single population is tempting. This can simplify future predictions and reduce uncertainty associated with estimation. However, combining these populations may introduce bias if the underlying relationships are in fact different. The probability of agreement formally and intuitively quantifies the similarity of estimated reliability surfaces across a two-factor input space. An example from the reliability literature demonstrates the utility of the approach when deciding whether to combine two populations or to keep them as distinct. New graphical summaries provide strategies for visualizing the results.

Kinetic Monte Carlo Methods For Computing First Capture Time Distributions In Models Of Diffusive Absorption, Daniel Schmidt

HMC Senior Theses

In this paper, we consider the capture dynamics of a particle undergoing a random walk above a sheet of absorbing traps. In particular, we seek to characterize the distribution in time from when the particle is released to when it is absorbed. This problem is motivated by the study of lymphocytes in the human blood stream; for a particle near the surface of a lymphocyte, how long will it take for the particle to be captured? We model this problem as a diffusive process with a mixture of reflecting and absorbing boundary conditions. The model is analyzed from two approaches. …

Stochastic Processes And Integrals, Jose L. Menaldi

Mathematics Faculty Research Publications

Stochastic integrals with respect to Wiener process and Poisson measures are discusses, beginning from stochastic processes.

Influences Of Probability Instruction On Undergraduates' Understanding Of Counting Processes, Kayla Blyman

Theses and Dissertations--Education Sciences

Historically, students in an introductory finite mathematics course at a major university in the mid-south have struggled the most with the counting and probability unit, leading instructors to question if there was a better way to help students master the material. The purpose of this study was to begin to understand connections that undergraduate finite mathematics students are making between counting and probability. By examining student performance in counting and probability, this study provides insights that inform future instruction in courses that include counting and probability. Consequently, this study lays the groundwork for future inquiries in the field of undergraduate …

A Traders Guide To The Predictive Universe- A Model For Predicting Oil Price Targets And Trading On Them, Jimmie Harold Lenz

Doctor of Business Administration Dissertations

At heart every trader loves volatility; this is where return on investment comes from, this is what drives the proverbial “positive alpha.” As a trader, understanding the probabilities related to the volatility of prices is key, however if you could also predict future prices with reliability the world would be your oyster. To this end, I have achieved three goals with this dissertation, to develop a model to predict future short term prices (direction and magnitude), to effectively test this by generating consistent profits utilizing a trading model developed for this purpose, and to write a paper that anyone with …

Newsvendor Models With Monte Carlo Sampling, Ijeoma W. Ekwegh

Electronic Theses and Dissertations

Newsvendor Models with Monte Carlo Sampling by Ijeoma Winifred Ekwegh The newsvendor model is used in solving inventory problems in which demand is random. In this thesis, we will focus on a method of using Monte Carlo sampling to estimate the order quantity that will either maximizes revenue or minimizes cost given that demand is uncertain. Given data, the Monte Carlo approach will be used in sampling data over scenarios and also estimating the probability density function. A bootstrapping process yields an empirical distribution for the order quantity that will maximize the expected profit. Finally, this method will be used …

Teaching The Quandary Of Statistical Jurisprudence: A Review-Essay On Math On Trial By Schneps And Colmez, Noah Giansiracusa

Journal of Humanistic Mathematics

This review-essay on the mother-and-daughter collaboration Math on Trial stems from my recent experience using this book as the basis for a college freshman seminar on the interactions between math and law. I discuss the strengths and weaknesses of this book as an accessible introduction to this enigmatic yet deeply important topic. For those considering teaching from this text (a highly recommended endeavor) I offer some curricular suggestions.

Simple Tools With Nontrivial Implications For Assessment Of Hypothesis-Evidence Relationships: The Interrogator’S Fallacy, Justus R. Riek

Journal of Humanistic Mathematics

This paper takes a mathematical analysis technique derived from the Interrogator’s Fallacy (in a legal context), expands upon it to identify a set of three interrelated probabilistic tools with wide applicability, and demonstrates their ability to assess hypothesis-evidence relationships associated with important problems

Stochastic Processes And Their Applications To Change Point Detection Problems, Heng Yang

Dissertations, Theses, and Capstone Projects

This dissertation addresses the change point detection problem when either the post-change distribution has uncertainty or the post-change distribution is time inhomogeneous. In the case of post-change distribution uncertainty, attention is drawn to the construction of a family of composite stopping times. It is shown that the proposed composite stopping time has third order optimality in the detection problem with Wiener observations and also provides information to distinguish the different values of post-change drift. In the case of post-change distribution uncertainty, a computationally efficient decision rule with low-complexity based on Cumulative Sum (CUSUM) algorithm is also introduced. In the time …

Thinking Poker Through Game Theory, Damian Palafox

Electronic Theses, Projects, and Dissertations

Poker is a complex game to analyze. In this project we will use the mathematics of game theory to solve some simplified variations of the game. Probability is the building block behind game theory. We must understand a few concepts from probability such as distributions, expected value, variance, and enumeration methods to aid us in studying game theory. We will solve and analyze games through game theory by using different decision methods, decision trees, and the process of domination and simplification. Poker models, with and without cards, will be provided to illustrate optimal strategies. Extensions to those models will be …

Elements Of The Mathematical Formulation Of Quantum Mechanics, Keunjae Go

Senior Honors Papers / Undergraduate Theses

In this paper, we will explore some of the basic elements of the mathematical formulation of quantum mechanics. In the first section, I will list the motivations for introducing a probability model that is quite different from that of the classical probability theory, but still shares quite a few significant commonalities. Later in the paper, I will discuss the quantum probability theory in detail, while paying a brief attention to some of the axioms (by Birkhoff and von Neumann) that illustrate both the commonalities and differences between classical mechanics and quantum mechanics. This paper will end with a presentation of …

Method For Determining Time-Resolved Heat Transfer Coefficient And Adiabatic Effectiveness Waveforms With Unsteady Film Cooling, James L. Rutledge, Jonathan F. Mccall

AFIT Patents

A new method for determining heat transfer coefficient (h) and adiabatic effectiveness (η) waveforms h(t) and η(t) from a single test uses a novel inverse heat transfer methodology to use surface temperature histories obtained using prior art approaches to approximate the h(t) and η(t) waveforms. The method best curve fits the data to a pair of truncated Fourier series.

Models For Hsv Shedding Must Account For Two Levels Of Overdispersion, Amalia Magaret

UW Biostatistics Working Paper Series

We have frequently implemented crossover studies to evaluate new therapeutic interventions for genital herpes simplex virus infection. The outcome measured to assess the efficacy of interventions on herpes disease severity is the viral shedding rate, defined as the frequency of detection of HSV on the genital skin and mucosa. We performed a simulation study to ascertain whether our standard model, which we have used previously, was appropriately considering all the necessary features of the shedding data to provide correct inference. We simulated shedding data under our standard, validated assumptions and assessed the ability of 5 different models to reproduce the …

Simulation Of Nuclear Fusion Using A One Dimensional Particle In Cell Method, Steven T. Margell

Cal Poly Humboldt theses and projects

In this thesis several novel techniques are developed to simulate fusion events in an isotropic, electrostatic three-dimensional Deuterium-Tritium plasma. These techniques allow us to accurately predict three-dimensional collision events with a one-dimensional model while simultaneously reducing compute time via a nearest neighbor algorithm. Furthermore, a fusion model based on first principles is developed that yields an average fusion reactivity which correlates well with empirical results.

Pcr5 And Neutrosophic Probability In Target Identification, Florentin Smarandache, Nassim Abbas, Youcef Chibani, Bilal Hadjadji, Zayen Azzouz Omar

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we use PCR5 in order to fusion the information of two sources providing subjective probabilities of an event A to occur in the following form: chance that A occurs, indeterminate chance of occurrence of A, chance that A does not occur.

A New Right Tailed Test Of The Ratio Of Variances, Elizabeth Rochelle Lesser

UNF Graduate Theses and Dissertations

It is important to be able to compare variances efficiently and accurately regardless of the parent populations. This study proposes a new right tailed test for the ratio of two variances using the Edgeworth’s expansion. To study the Type I error rate and Power performance, simulation was performed on the new test with various combinations of symmetric and skewed distributions. It is found to have more controlled Type I error rates than the existing tests. Additionally, it also has sufficient power. Therefore, the newly derived test provides a good robust alternative to the already existing methods.

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 …