Probability Commons^™

Utility In Time Description In Priority Best-Worst Discrete Choice Models: An Empirical Evaluation Using Flynn's Data, Sasanka Adikari, Norou Diawara

Mathematics & Statistics Faculty Publications

Discrete choice models (DCMs) are applied in many fields and in the statistical modelling of consumer behavior. This paper focuses on a form of choice experiment, best-worst scaling in discrete choice experiments (DCEs), and the transition probability of a choice of a consumer over time. The analysis was conducted by using simulated data (choice pairs) based on data from Flynn's (2007) 'Quality of Life Experiment'. Most of the traditional approaches assume the choice alternatives are mutually exclusive over time, which is a questionable assumption. We introduced a new copula-based model (CO-CUB) for the transition probability, which can handle the dependent …

Statistical Approach To Quantifying Interceptability Of Interaction Scenarios For Testing Autonomous Surface Vessels, Benjamin E. Hargis, Yiannis E. Papelis

Modeling, Simulation and Visualization Student Capstone Conference

This paper presents a probabilistic approach to quantifying interceptability of an interaction scenario designed to test collision avoidance of autonomous navigation algorithms. Interceptability is one of many measures to determine the complexity or difficulty of an interaction scenario. This approach uses a combined probability model of capability and intent to create a predicted position probability map for the system under test. Then, intercept-ability is quantified by determining the overlap between the system under test probability map and the intruder’s capability model. The approach is general; however, a demonstration is provided using kinematic capability models and an odometry-based intent model.

An Adaptive Algorithm For `The Secretary Problem': Alternate Proof Of The Divergence Of A Maximizer Sequence, Andrew Benfante, Xiang Xu

OUR Journal: ODU Undergraduate Research Journal

This paper presents an alternate proof of the divergence of the unique maximizer sequence {𝑥∗ 𝑛} of a function sequence {𝐹𝑛(𝑥)} that is derived from an adaptive algorithm based on the now classic optimal stopping problem, known by many names but here ‘the secretary problem’. The alternate proof uses a result established by Nguyen, Xu, and Zhao (n.d.) regarding the uniqueness of maximizer points of a generalized function sequence {𝑆𝜇,𝜎 𝑛 } and relies on the strict monotonicity of 𝐹𝑛(𝑥) as 𝑛 increases in order to show divergence of {𝑥∗ 𝑛}. Towards this, limits of the exponentiated Gaussian CDF are …

Em Estimation For Zero- And K-Inflated Poisson Regression Model, Monika Arora, N. Rao Chaganty

Mathematics & Statistics Faculty Publications

Count data with excessive zeros are ubiquitous in healthcare, medical, and scientific studies. There are numerous articles that show how to fit Poisson and other models which account for the excessive zeros. However, in many situations, besides zero, the frequency of another count k tends to be higher in the data. The zero- and k-inflated Poisson distribution model (ZkIP) is appropriate in such situations The ZkIP distribution essentially is a mixture distribution of Poisson and degenerate distributions at points zero and k. In this article, we study the fundamental properties of this mixture distribution. Using stochastic representation, we …

D-Vine Copula Model For Dependent Binary Data, Huihui Lin, N. Rao Chaganty

College of Sciences Posters

High-dimensional dependent binary data are prevalent in a wide range of scientific disciplines. A popular method for analyzing such data is the Multivariate Probit (MP) model. But the MP model sometimes fails even within a feasible range of binary correlations, because the underlying correlation matrix of the latent variables may not be positive definite. In this research, we proposed pair copula models, assuming the dependence between the binary variables is first order autoregressive (AR(1))or equicorrelated structure. Also, when Archimediean copula is used, most paper converted Kendall Tau to corresponding copula parameter, there is no explicit function of Pearson’s correlation coefficient …

Dynamic Attribute-Level Best Worst Discrete Choice Experiments, Amanda Working, Mohammed Alqawba, Norou Diawara

Mathematics & Statistics Faculty Publications

Dynamic modelling of decision maker choice behavior of best and worst in discrete choice experiments (DCEs) has numerous applications. Such models are proposed under utility function of decision maker and are used in many areas including social sciences, health economics, transportation research, and health systems research. After reviewing references on the study of such experiments, we present example in DCE with emphasis on time dependent best-worst choice and discrimination between choice attributes. Numerical examples of the dynamic DCEs are simulated, and the associated expected utilities over time of the choice models are derived using Markov decision processes. The estimates are …

Density Estimation Of Spatio-Temporal Point Patterns Using Moran’S Statistics, Jennifer L. Lorio, Norou Diawara, Lance A. Waller

Mathematics & Statistics Faculty Publications

Moran’s Index is a statistic that measures spatial autocorrelation, quantifying the degree of dispersion (or spread) of objects in space. When investigating data in an area, a single Moran statistic may not give a sufficient summary of the autocorrelation spread. However, by partitioning the area and taking the Moran statistic of each subarea, we discover patterns of the local neighbors not otherwise apparent. In this paper, we consider the model of the spread of an infectious disease, incorporate time factor, and simulate a multilevel Poisson process where the dependence among the levels is captured by the rate of increase of …

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 …

Response Surface Optimization Of Electron Beam Freeform Fabrication Depositions Using Design Of Experiments, Patricia A. Quigley

Engineering Management & Systems Engineering Theses & Dissertations

The Electron Beam Freeform Fabrication (EBF³ ) System is a material depositing, layer additive technique that produces three dimensional (3D) parts out of a wide range of metals in high vacuum, using an electron beam and wire feedstock. Screening deposition trials on a titanium alloy, Ti-6Al-4V, at the National Aeronautics Space Administration (NASA) revealed selective vaporization of the aluminum content of linear prototypes when subjected to chemical analysis. In this study, the aluminum content, bead height and bead width output responses were analyzed from a systematic study of the effects that the interactions of the EBF³ processing parameters …

Drag Reduction Of A Modern Straight Truck, Drew Landman, Matthew Cragun, Mike Mccormick, Richard Wood

Mechanical & Aerospace Engineering Faculty Publications

A wind tunnel test program was conducted at the Langley Full Scale Tunnel (LFST) to evaluate the performance of five passive drag reduction configurations on a modern straight truck at full scale. Configurations were tested in a build-up fashion with results representing a cumulative effect. Tested configurations include a front valance, a front box fairing, a boat-tail, an ideal side-skirt, and a practical side-skirt. Configurations were evaluated over a nominal 9 degree yaw sweep to establish wind averaged drag coefficients using SAE J1252. Genuine replicate yaw sweeps were used in an uncertainty analysis. Results show up to 28% improvement in …

Probability Models For Blackjack Poker, Charlie H. Cooke

Mathematics & Statistics Faculty Publications

For simplicity in calculation, previous analyses of blackjack poker have employed models which employ sampling with replacement. in order to assess what degree of error this may induce, the purpose here is to calculate results for a typical hand where sampling without replacement is employed. It is seen that significant error can result when long runs are required to complete the hand. The hand examined is itself of particular interest, as regards both its outstanding expectations of high yield and certain implications for pair splitting of two nines against the dealer's seven. Theoretical and experimental methods are used in order …

The Joint Distribution Of Bivariate Exponential Under Linearly Related Model, Norou Diawara, Kumer Pial Das

Mathematics & Statistics Faculty Publications

In this paper, fundamental results of the joint distribution of the bivariate exponential distributions are established. The positive support multivariate distribution theory is important in reliability and survival analysis, and we applied it to the case where more than one failure or survival is observed in a given study. Usually, the multivariate distribution is restricted to those with marginal distributions of a specified and familiar lifetime family. The family of exponential distribution contains the absolutely continuous and discrete case models with a nonzero probability on a set of measure zero. Examples are given, and estimators are developed and applied to …

Linear Dependency For The Difference In Exponential Regression, Indika Sathish, Norou Diawara

Mathematics & Statistics Faculty Publications

In the field of reliability, a lot has been written on the analysis of phenomena that are related. Estimation of the difference of two population means have been mostly formulated under the no-correlation assumption. However, in many situations, there is a correlation involved. This paper addresses this issue. A sequential estimation method for linearly related lifetime distributions is presented. Estimations for the scale parameters of the exponential distribution are given under square error loss using a sequential prediction method. Optimal stopping rules are discussed using concepts of mean criteria, and numerical results are presented.

Uncertainty Assessment Of Aircraft Maintenance Times By Using Evidence Theory And Expert Judgment Elicitation, Huseyin Kudak

Engineering Management & Systems Engineering Theses & Dissertations

The goal of this study is to demonstrate the use of the Dempster-Shafer Theory of evidence as a decision aid to predict aircraft maintenance times during wartime operations using expert judgment elicitation. Increased precision in time estimation enables the jet engine aircraft maintenance facility commander to make more accurate decisions for the Air Force's wartime tactical operations allowing the commander to gain a decisive advantage. A questionnaire was designed to elicit judgments from experts in the Aircraft Maintenance Facility (AMF) to investigate maintenance times of the major failure modes (Ignition, Fuel, and Electrical). Results of the expert judgment elicitation were …

Radical Impact Of Change In Actions And Confidence Index On Reverse Decision Making An Application Based Study, Swatee Trimbak Paithankar

Engineering Management & Systems Engineering Theses & Dissertations

While making decisions under uncertainty, people are often unaware of the logical approach to form the decision process. It is assumed that collecting details, analyzing and evaluating data is enough to make 'proper' decisions. However, past research in the decision making arena has significantly validated that there exists a class of decision problems which is complex, ill-structured and not defined to the level where decision makers can draw logical conclusions based on existing traditional decision approaches. RDM (reverse decision making), one of the novel approaches of decision making under conditions of uncertainty, has shown potential towards addressing some of these …

Modeling And Efficient Estimation Of Intra-Family Correlations, Roy Sabo

Mathematics & Statistics Theses & Dissertations

Familial data occur when observations are taken on multiple members of the same family. Due to relationships between these members, both genetic and by cohabitation, their response variables will likely exhibit some form of dependence. Most of the existing literature models this dependence with an equicorrelated structure. This structure is appropriate when the dependencies between family members are similar, such as in genetic studies, but not in cases where we expect the dependencies to differ, such as behavioral comparisons across different age groups. In this dissertation we first discuss an alternative structure based upon first-order autoregressive correlation. Specifically we create …

Single Row Routing: Theoretical And Experimental Performance Evaluation, And New Heuristic Development, David A. Hysom

Computer Science Theses & Dissertations

The Single Row Routing Problem (SRRP) is an abstraction arising from real-world multilayer routing concerns. While NP-Complete, development of efficient SRRP routing heuristics are of vital concern to VLSI design. Previously, researchers have introduced various heuristics for SRRP; however, a comprehensive examination of SRRP behavior has been lacking.

We are particularly concerned with the street-congestion minimization constraint, which is agreed to be the constraint of greatest interest to industry. Several theorems stating lower bounds on street congestion are known. We show that these bounds are not tight in general, and argue they may be in error by at least 50% …

Impact Of Field-Dependent Electronic Trapping Across Coulomb Repulsive Potentials On Low Frequency Charge Oscillations, R. P. Joshi, K. H. Schoenbach, P. K. Raha

Bioelectrics Publications

We have performed Monte Carlo simulations to obtain the field dependence of electronic trapping across repulsive potentials in GaAs. Such repulsive centers are associated with deep level impurities having multiply charged states. Our results reveal a field‐dependent maxima in the electronic capture coefficient, and the overall shape is seen to depend on the background electron density due to the effects of screening. Based on the Monte Carlo calculations, we have examined the stability of compensated semiconductors containing such repulsive centers. Our analysis indicates a potential for low frequency charge oscillations which is in keeping with available experimental data.

Studies Of Electron-Beam Penetration And Free-Carrier Generation In Diamond Films, R. P. Joshi, K. H. Schoenbach, C. Molina, W. W. Hofer

Bioelectrics Publications

Experimental observations of the energy‐dependent electron‐beam penetration in type II‐A natural diamond are reported. The experimental data are compared with results obtained from numerical Monte Carlo simulations, and the results are in very good agreement. The results also reveal that a threshold energy of about 125 keV is necessary for complete penetration for a 35 μm sample. It is found that over the 30–180 keV range, the energy dependence of the penetration depth and total path length exhibits a power‐law relation. Monte Carlo simulations have also been performed to investigate the excess carrier‐generation profiles within diamond for a set of …

Estimation In A Marked Poisson Error Recapture Model Of Software Reliability, Rajan Gupta

Mathematics & Statistics Theses & Dissertations

Nayak's (1988) model for the detection, removal, and recapture of the errors in a computer program is extended to a larger family of models in which the probabilities that the successive programs produce errors are described by the tail probabilities of discrete distribution on the positive integers. Confidence limits are derived for the probability that the final program produces errors. A comparison of the asymptotic variances of parameter estimates given by the error recapture and by the repetitive-run procedure of Nagel, Scholz, and Skrivan (1982) is made to determine which of these procedures efficiently uses the test time.

A Model Of Dc Glow Discharges With Abnormal Cathode Fall, Karl H. Schoenbach, Hao Chen, G. Schaefer

Bioelectrics Publications

A model for an abnormal glow discharge, including a self‐consistent analysis of the cathode fall, was developed. It combines microscopic particle simulation by means of Monte Carlo methods with a fluid model of the gas discharge. The model allows calculations of the steady‐state electrical field distribution, the charged‐particle densities, and the current densities along the axis of the discharge. The model was used to simulate a glow discharge in 80% He and 20% SF₆ at a pressure of 8 Torr with a current density of 1 A/cm². The computed discharge voltage agrees well with measured values. The …

Large Deviation Local Limit Theorems For Ratio Statistics, Sanjeev V. Sabnis

Mathematics & Statistics Theses & Dissertations

Let {T„, n > 1} be an arbitrary sequence of non-lattice random variables and {S_n, n > 1} be another sequence of positive non-lattice random variables. Let the two sequences be independent. Let Ø_1n and Ø_2n be the moment genereating functions of {Tn, n > 1} and { S_n,n > 1} respectively. Let {a_n} be a sequence of real numbers such that a_n —»• oo.

Limit Theorems In The Area Of Large Deviations For Some Dependent Random Variables, Narasinga Rao Chaganty, Jayaram Sethuraman

Mathematics & Statistics Faculty Publications

A magnetic body can be considered to consist of n sites, where n is large. The magnetic spins at these n sites, whose sum is the total magnetization present in the body, can be modelled by a triangular array of random variables (X(n) 1,..., X(n) n). Standard theory of physics would dictate that the joint distribution of the spins can be modelled by dQ_n(x) = z_n^-1 exp[ -H_n(x)]Π dP(x_j), where x = (x₁,..., x_n) ∈ Rⁿ, where H_n is the Hamiltonian, z_n is …

On The First Passage Time Distribution For A Class Of Markov Chains, Mark Brown, Narasinga Rao Chaganty

Mathematics & Statistics Faculty Publications

Consider a stochastically monotone chain with monotone paths on a partially ordered countable set S. Let C be an increasing subset of S with finite complement. Then the first passage-time from i ∈ S to C is shown to be IFRA (increasing failure rate on the,av;rage). Several applications are presented including coherent systems, shock models, and convolutions of IFRA distributions.