Probability Commons^™

(R1971) Analysis Of Feedback Queueing Model With Differentiated Vacations Under Classical Retrial Policy, Poonam Gupta, Naveen Kumar, Rajni Gupta

Applications and Applied Mathematics: An International Journal (AAM)

This paper analyzes an M/M/1 retrial queue under differentiated vacations and Bernoulli feedback policy. On receiving the service, if the customer is not satisfied, then he may join the retrial group again with some probability and demand for service or may leave the system with the complementary probability. Using the probability generating functions technique, the steady-state solutions of the system are obtained. Furthermore, we have obtained some of the important performance measures such as expected orbit length, expected length of the system, sojourn times and probability of server being in different states. Using MATLAB software, we have represented the graphical …

(R1984) Analysis Of M^[X1], M^[X2]/G1, G_2^(A,B)/1 Queue With Priority Services, Server Breakdown, Repair, Modified Bernoulli Vacation, Immediate Feedback, G. Ayyappan, S. Nithya, B. Somasundaram

Applications and Applied Mathematics: An International Journal (AAM)

In this investigation, the steady state analysis of two individualistic batch arrival queues with immediate feedback, modified Bernoulli vacation and server breakdown are introduced. Two different categories of customers like priority and ordinary are to be considered. This model propose nonpreemptive priority discipline. Ordinary and priority customers arrive as per Poisson processes. The server consistently afford single service for priority customers and the general bulk service for the ordinary customers and the service follows general distribution. The ordinary customers to be served only if the batch size should be greater than or equal to "a", else the server should not …

(R1999) Analysis Of A Markovian Retrial Queue With Reneging And Working Vacation Under N-Control Pattern, P. Manoharan, S. Pazhani Bala Murugan, A. Sobanappriya

Applications and Applied Mathematics: An International Journal (AAM)

A Markovian retrial queue with reneging and working vacation under N-control pattern is investigated in this article. To describe the system, we employ a QBD analogy. The model’s stability condition is deduced. The stationary probability distribution is gotten by utilizing the matrix-analytic technique. The conditional stochastic decomposition of the line length in the orbit is calculated. The performance measures and special cases are designed. The model’s firmness is demonstrated numerically.

(R1974) A Multi Server Markovian Working Vacation Queue With Server State Dependent Rates And With Partial Breakdown, A. Sundaramoorthy, R. Kalyanaraman

Applications and Applied Mathematics: An International Journal (AAM)

In this article, we consider an M/M/C queue in which the arrival rate and service rate depends on the state of the system. In addition, the servers takes working vacation and the system may breakdown. Whenever breakdown takes place, the repair process immediately commences. During the repair period the customers are given service in a reduced service rate. Based on the vacation termination point, two models have been defined. The steady state probability vector of the number of customers in the queue and the stability condition are obtained using Matrix-Geometric method. The stationary waiting time distributions have been obtained. Some …

(Si10-083) Approximate Controllability Of Infinite-Delayed Second-Order Stochastic Differential Inclusions Involving Non-Instantaneous Impulses, Shobha Yadav, Surendra Kumar

Applications and Applied Mathematics: An International Journal (AAM)

This manuscript investigates a broad class of second-order stochastic differential inclusions consisting of infinite delay and non-instantaneous impulses in a Hilbert space setting. We first formulate a new collection of sufficient conditions that ensure the approximate controllability of the considered system. Next, to investigate our main findings, we utilize stochastic analysis, the fundamental solution, resolvent condition, and Dhage’s fixed point theorem for multi-valued maps. Finally, an application is presented to demonstrate the effectiveness of the obtained results.

Public Acceptance Of Medical Screening Recommendations, Safety Risks, And Implied Liabilities Requirements For Space Flight Participation, Cory J. Trunkhill

Doctoral Dissertations and Master's Theses

The space tourism industry is preparing to send space flight participants on orbital and suborbital flights. Space flight participants are not professional astronauts and are not subject to the rules and guidelines covering space flight crewmembers. This research addresses public acceptance of current Federal Aviation Administration guidance and regulations as designated for civil participation in human space flight.

The research utilized an ordinal linear regression analysis of survey data to explore the public acceptance of the current medical screening recommended guidance and the regulations for safety risk and implied liability for space flight participation. Independent variables constituted participant demographic representations …

Machine Learning To Predict Warhead Fragmentation In-Flight Behavior From Static Data, Katharine Larsen

Doctoral Dissertations and Master's Theses

Accurate characterization of fragment fly-out properties from high-speed warhead detonations is essential for estimation of collateral damage and lethality for a given weapon. Real warhead dynamic detonation tests are rare, costly, and often unrealizable with current technology, leaving fragmentation experiments limited to static arena tests and numerical simulations. Stereoscopic imaging techniques can now provide static arena tests with time-dependent tracks of individual fragments, each with characteristics such as fragment IDs and their respective position vector. Simulation methods can account for the dynamic case but can exclude relevant dynamics experienced in real-life warhead detonations. This research leverages machine learning methodologies to …

Application Of Probabilistic Ranking Systems On Women’S Junior Division Beach Volleyball, Cameron Stewart, Michael Mazel, Bivin Sadler

SMU Data Science Review

Women’s beach volleyball is one of the fastest growing collegiate sports today. The increase in popularity has come with an increase in valuable scholarship opportunities across the country. With thousands of athletes to sort through, college scouts depend on websites that aggregate tournament results and rank players nationally. This project partnered with the company Volleyball Life, who is the current market leader in the ranking space of junior beach volleyball players. Utilizing the tournament information provided by Volleyball Life, this study explored replacements to the current ranking systems, which are designed to aggregate player points from recent tournament placements. Three …

Defining Viable Solar Resource Locations In The Southeast United States Using The Satellite-Based Glass Product, Jolie Kavanagh

Theses and Dissertations

This research uses satellite data and the moment statistics to determine if solar farms can be placed in the Southeast US. From 2001-2019, the data are analyzed in reference to the Southwest US, where solar farms are located. The clean energy need is becoming more common; therefore, more locations than arid environments must be observed. The Southeast US is the main location of interest due to the warm, moist environment throughout the year. This research uses the Global Land Surface Satellite (GLASS) photosynthetically active radiation product (PAR) to determine viable locations for solar panels. A probability density function (PDF) along …

Random Walks In The Quarter Plane: Solvable Models With An Analytical Approach, Harshita Bali, Enrico Au-Yeung

DePaul Discoveries

Initially, an urn contains 3 blue balls and 1 red ball. A ball is randomly chosen from the urn. The ball is returned to the urn, together with one additional ball of the same type (red or blue). When the urn has twenty balls in it, what is the probability that exactly ten balls are blue? This is a model for a random process. This urn model has been extended in various ways and we consider some of these generalizations. Urn models can be formulated as random walks in the quarter plane. Our findings indicate that for a specific type …

Effect Of Monetary Policy Rate On Market Interest Rates In Nigeria: A Threshold And Nardl Approach, Oluwafemi E. Awopegba, Joseph O. Afolabi, Lydia T. Adeoye, Godwin O. Akpokodje

CBN Journal of Applied Statistics (JAS)

This study examines the effect of monetary policy rate (MPR) on market interest rates in Nigeria. For parsimony, we develop two indexes called the short-term interest rate (SINT) and Lending interest rate (LINT) to represent deposit and lending rates respectively. The nonlinear autoregressive distributed lag (NARDL) and threshold regression models are adopted. The study uses monthly data from 2002:M1 to 2019:M12. The results of the threshold regression model indicate that the degree of the effect of MPR on SINT and LINT above the estimated threshold of 11 and 13 percent respectively is greater and significant than if MPR were to …

Social Dimension Of Inclusive Growth In Ecowas: Implication For Poverty Reduction, Toriola K. Anu, Goerge O. Emmanuel, Ajayi O. Felix

CBN Journal of Applied Statistics (JAS)

This study investigates the implication of the social dimension of inclusive growth on poverty reduction in Economic Community of West African States (ECOWAS) countries. It specifically examines how social indices of inclusive growth comprising of income inequality, education, and health outcomes affect poverty reduction. The study uses a panel dataset of the six (6) lower-middle income countries in ECOWAS which was analysed via panel Difference Generalised Method of Moment (D-GMM). The results show that GDP per capita exerts significant negative effect on poverty while inequality, education and health outcomes do not show significant effect on poverty. Although, the estimates of …

Effect Of Fdi Inflows On Employment Generation In Selected Ecowas Countries: Heterogeneous Panel Analysis, Timothy A. Aderemi, Olawunmi Omitogun, Bukonla G. Osisanwo

CBN Journal of Applied Statistics (JAS)

The aim of this study is to examine the effect of FDI on employment in ECOWAS sub region between 1990 and 2019. The study utilizes a panel autoregressive distributed lag model to analyse the short run and long run relationship between FDI and employment across ECOWAS sub region. In the short run, the impact of FDI on employment is negative and statistically not significant. Meanwhile, in the long run FDI has a positive and statistically significant impact on employment rate. This implies that FDI has the capacity to generate employment in countries in ECOWAS sub region. Therefore, this study recommends …

Impact Of Covid-19 Pandemic On The Nigeria Stock Market: A Sectoral Stock Prices Analysis, Peter A. Adekunle, Yakubu A. Bello, Udochukwu G. Nwachukwu

CBN Journal of Applied Statistics (JAS)

This study examines the impact of the COVID-19 pandemic on sectoral stock prices in Nigeria stock market using daily data covering from February 28, 2020 to June 26, 2020. Applying the autoregressive distributed lag (ARDL) bounds test, the study finds that COVID-19 pandemic had adverse impact on the stock market indices in the short run. Furthermore, the study documents negative response of sectoral stock prices to the pandemic while the stock prices of the banking sub-sector are the worst hit. Compared to the consumer goods, and industrial subsector indices, the speed of adjustment to long run equilibrium is faster for …

Rewriting The Rules For Diagnostics: Implications Of Probability And Measure Theory For Sars-Cov-2 Testing, Paul Patrone, Anthony Kearsley

Biology and Medicine Through Mathematics Conference

No abstract provided.

Optimal Time-Dependent Classification For Diagnostic Testing, Prajakta P. Bedekar, Paul Patrone, Anthony Kearsley

Biology and Medicine Through Mathematics Conference

No abstract provided.

Some Improved Markov Chain Convergence Rates, Fun Choi John Chan

All Dissertations

Explicit convergence rates to equilibrium are established for non reversible Markov chains not having an atom via coupling methods. We consider two Markov chains having the same transition function but different initial conditions on the same probability space, that is, a coupling. A random time is constructed so that subsequent to the random time the two processes are identical. Exploiting a shadowing condition, we show that it is possible to bound the tail distribution of the random time using only one of the chains. This bound gives the convergence rate to equilibrium for the Markov chain. The method is then …

Advancements In Gaussian Process Learning For Uncertainty Quantification, John C. Nicholson

All Dissertations

Gaussian processes are among the most useful tools in modeling continuous processes in machine learning and statistics. The research presented provides advancements in uncertainty quantification using Gaussian processes from two distinct perspectives. The first provides a more fundamental means of constructing Gaussian processes which take on arbitrary linear operator constraints in much more general framework than its predecessors, and the other from the perspective of calibration of state-aware parameters in computer models. If the value of a process is known at a finite collection of points, one may use Gaussian processes to construct a surface which interpolates these values to …

Percentage Of Yellow Sour Patch Kids, Easton Kratzer, Sarah Baxter

Harrisburg University Research Symposium: Highlighting Research, Innovation, & Creativity

After being given the Qualitative Research Project in Introduction to Statistics, I came up with the question asking what percentage of Sour Patch Kids are yellow. This resulted in me going through an entire bag and counting the amount of every color to figure out the percentages. (Class Project)

Preference For Violence By Gender, Ayrton Hall, Christian Watson, Akeisha Belgrave

Harrisburg University Research Symposium: Highlighting Research, Innovation, & Creativity

In our survey we asked students of HU what their favorite video games were as well as their favorite genre and most played game. We then analyzed the data to see how gender affects preference for violent games. (Class Project)

Favorite Programming Language Among Students, Anwar Jawhar, Akeisha Belgrave

Harrisburg University Research Symposium: Highlighting Research, Innovation, & Creativity

This project involves understanding the favorite programming language among students. I hypothesize that the favorite programming language will be Python. (Class Project)

Anticipating Stochastic Integrals And Related Linear Stochastic Differential Equations, Sudip Sinha

LSU Doctoral Dissertations

Itô’s stochastic calculus revolutionized the field of stochastic analysis and has found numerous applications in a wide variety of disciplines. Itô’s theory, even though quite general, cannot handle anticipating stochastic processes as integrands. There have been considerable efforts within the mathematical community to extend Itô’s calculus to account for anticipation. The Ayed–Kuo integral — introduced in 2008 — is one of the most recent developments. It is arguably the most accessible among the theories extending Itô’s calculus — relying solely on probabilistic methods. In this dissertation, we look at the recent advances in this area, highlighting our contributions. First, we …

General Stochastic Calculus And Applications, Pujan Shrestha

LSU Doctoral Dissertations

In 1942, K. Itô published his pioneering paper on stochastic integration with respect to Brownian motion. This work led to the framework for Itô calculus. Note that, Itô calculus is limited in working with knowledge from the future. There have been many generalizations of the stochastic integral in being able to do so. In 2008, W. Ayed and H.-H. Kuo introduced a new stochastic integral by splitting the integrand into the adaptive part and the counterpart called instantly independent. In this doctoral work, we conduct deeper research into the Ayed–Kuo stochastic integral and corresponding anticipating stochastic calculus.

We provide a …

Intra-Hour Solar Forecasting Using Cloud Dynamics Features Extracted From Ground-Based Infrared Sky Images, Guillermo Terrén-Serrano

Electrical and Computer Engineering ETDs

Due to the increasing use of photovoltaic systems, power grids are vulnerable to the projection of shadows from moving clouds. An intra-hour solar forecast provides power grids with the capability of automatically controlling the dispatch of energy, reducing the additional cost for a guaranteed, reliable supply of energy (i.e., energy storage). This dissertation introduces a novel sky imager consisting of a long-wave radiometric infrared camera and a visible light camera with a fisheye lens. The imager is mounted on a solar tracker to maintain the Sun in the center of the images throughout the day, reducing the scattering effect produced …

Session 5: Equipment Finance Credit Risk Modeling - A Case Study In Creative Model Development & Nimble Data Engineering, Edward Krueger, Landon Thompson, Josh Moore

SDSU Data Science Symposium

This presentation will focus first on providing an overview of Channel and the Risk Analytics team that performed this case study. Given that context, we’ll then dive into our approach for building the modeling development data set, techniques and tools used to develop and implement the model into a production environment, and some of the challenges faced upon launch. Then, the presentation will pivot to the data engineering pipeline. During this portion, we will explore the application process and what happens to the data we collect. This will include how we extract & store the data along with how it …

Probability Models With Discrete And Continuous Parts, James E. Marengo, David L. Farnsworth

Articles

In mathematical statistics courses, students learn that the quadratic function E ((X – x )-squared) is minimized when x is the mean of the random variable X, and that the graphs of this function for any two distributions of X are simply translates of each other. We focus on the problem of minimizing the function defined by y ( x) = E ( IX – xI-squared ) in the context of mixtures of probability distributions of the discrete, absolutely continuous, and singular continuous types. This problem is important, for example, in Bayesian statistics, when one attempts to compute the decision …

Mathematically Modeling Prey-Catching Behavior Of The Tomato Frog, Conrad Tyler, Sarah Marzen, Jenna Monroy

Spora: A Journal of Biomathematics

Many microhylid frog species, such as the tomato frog, Dyscophus sp., have demonstrated the ability to aim their tongues independently of head and jaw movements. However, a trade-off between tongue-aiming and head-only aiming exists in which the former allows for crypsis but lacks speed whereas the latter is faster but less accurate and more noticeable to prey. For frogs that can move their tongues independently of their heads, under what circumstances will they utilize each strategy, and why? We derive a model, dependent on factors relevant for prey-catching, for the probability the frog will turn its head (and not …

Maximum Likelihood Estimator Method To Estimate Flaw Parameters For Different Glass Types, Nabhajit Goswami

Dissertations, Master's Theses and Master's Reports

Glass is commonly used in architectural applications, such as windows and in-fill panels and structural applications, such as beams and staircases. Despite the popularity of structural glass use in buildings, an engineering design standard to determine the required component or member strength for design loads does not exist. Glass is a brittle material that lacks a well-defined yield or ultimate stress, unlike ductile materials. The traditional engineering methods used to design a ductile material cannot be used to design a glass component. Glass fails in tension primarily due to the presence of microscopic flaws present on the surface that acts …

Analysis Of Minor League Rule Changes Effect On Stolen Bases, Zachary Houghtaling

Williams Honors College, Honors Research Projects

This study uses various statistical analyses to evaluate the justification of rule changes for Major League Baseball that were implemented within the Minor Leagues during the 2021 minor league season. The primary focus of the study is predicting how some of these Minor League rule changes could affect the stolen base success rate and the number of attempts per game within the Major Leagues. A survey was conducted to evaluate how fans feel about stolen bases within the current game and if rules should be altered to increase the number of stolen bases that occur. Additionally, recorded Major and Minor …

Searching For Anomalous Extensive Air Showers Using The Pierre Auger Observatory Fluorescence Detector, Andrew Puyleart

Dissertations, Master's Theses and Master's Reports

Anomalous extensive air showers have yet to be detected by cosmic ray observatories. Fluorescence detectors provide a way to view the air showers created by cosmic rays with primary energies reaching up to hundreds of EeV . The resulting air showers produced by these highly energetic collisions can contain features that deviate from average air showers. Detection of these anomalous events may provide information into unknown regions of particle physics, and place constraints on cross-sectional interaction lengths of protons. In this dissertation, I propose measurements of extensive air shower profiles that are used in a machine learning pipeline to distinguish …