Statistics and Probability Commons^™

The Efficient Use Of Supplementary Information In Finite Population Sampling, Florentin Smarandache, Rajesh Singh

Branch Mathematics and Statistics Faculty and Staff Publications

The purpose of writing this book is to suggest some improved estimators using auxiliary information in sampling schemes like simple random sampling, systematic sampling and stratified random sampling. This volume is a collection of five papers, written by nine co-authors (listed in the order of the papers): Rajesh Singh, Mukesh Kumar, Manoj Kr. Chaudhary, Cem Kadilar, Prayas Sharma, Florentin Smarandache, Anil Prajapati, Hemant Verma, and Viplav Kr. Singh. In first paper dual to ratio-cum-product estimator is suggested and its properties are studied. In second paper an exponential ratio-product type estimator in stratified random sampling is proposed and its properties are …

Fusion Of Masses Defined On Infinite Countable Frames Of Discernment, Florentin Smarandache, Arnaud Martin

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we introduce for the first time the fusion of information on infinite discrete frames of discernment and we give general results of the fusion of two such masses using the Dempster’s rule and the PCR5 rule for Bayesian and non-Bayesian cases.

A General Procedure Of Estimating Population Mean Using Information On Auxiliary Attribute, Sachin Malik, Rajesh Singh, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This paper deals with the problem of estimating the finite population mean when some information on auxiliary attribute is available. It is shown that the proposed estimator is more efficient than the usual mean estimator and other existing estimators. The results have been illustrated numerically by taking empirical population considered in the literature.

A Generalized Family Of Estimators For Estimating Population Mean Using Two Auxiliary Attributes, Sachin Malik, Rajesh Singh, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This paper deals with the problem of estimating the finite population mean when some information on two auxiliary attributes are available. A class of estimators is defined which includes the estimators recently proposed by Malik and Singh (2012), Naik and Gupta (1996) and Singh et al. (2007) as particular cases. It is shown that the proposed estimator is more efficient than the usual mean estimator and other existing estimators. The study is also extended to two-phase sampling. The results have been illustrated numerically by taking empirical population considered in the literature.

Building A Predictive Model For Baseball Games, Jordan Robertson Tait

All Graduate Theses, Dissertations, and Other Capstone Projects

In this paper, we will discuss a method of building a predictive model for Major League Baseball Games. We detail the reasoning for pursuing the proposed predictive model in terms of social popularity and the complexity of analyzing individual variables. We apply a coarse-grain outlook inspired by Simon Dedeos' work on Human Social Systems, in particular the open source website Wikipedia [2] by attempting to quantify the influence of winning and losing streaks instead of analyzing individual performance variables. We will discuss initial findings of data collected from the LA Dodgers and Colorado Rockies and apply further statistical analysis to …

A Statistical Fmri Model For Differential T2* Contrast Incorporating T1 And T2* Of Gray Matter, M. Muge Karaman, Iain P. Bruce, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

Relaxation parameter estimation and brain activation detection are two main areas of study in magnetic resonance imaging (MRI) and functional magnetic resonance imaging (fMRI). Relaxation parameters can be used to distinguish voxels containing different types of tissue whereas activation determines voxels that are associated with neuronal activity. In fMRI, the standard practice has been to discard the first scans to avoid magnetic saturation effects. However, these first images have important information on the MR relaxivities for the type of tissue contained in voxels, which could provide pathological tissue discrimination. It is also well-known that the voxels located in gray matter …

Trivial Meet And Join Within The Lattice Of Monotone Triangles, John Engbers, Adam Hammett

Mathematics, Statistics and Computer Science Faculty Research and Publications

The lattice of monotone triangles (�_n, ≼) ordered by entry-wise comparisons is studied. Let τ_min denote the unique minimal element in this lattice, and τ_max the unique maximum. The number of r-tuples of monotone triangles (τ₁...,τ_r) with minimul infimum τ_min (maximul supremum τ_max, resp.) is shown to asymptotically approach r|�_n|^r-1 as n→ ∞. Thus, with high probability this even implies that one of the τ_i is τ_min (τ_max, resp.). Higher-order error terms are also discussed.

Master Regulators, Regulatory Networks, And Pathways Of Glioblastoma Subtypes, Serdar Bozdag, Aiguo Li, Mehmet Baysan, Howard A. Fine

Mathematics, Statistics and Computer Science Faculty Research and Publications

Glioblastoma multiforme (GBM) is the most common malignant brain tumor. GBM samples are classified into subtypes based on their transcriptomic and epigenetic profiles. Despite numerous studies to better characterize GBM biology, a comprehensive study to identify GBM subtype-specific master regulators, gene regulatory networks, and pathways is missing. Here, we used FastMEDUSA to compute master regulators and gene regulatory networks for each GBM subtype. We also ran Gene Set Enrichment Analysis and Ingenuity Pathway Analysis on GBM expression dataset from The Cancer Genome Atlas Project to compute GBM- and GBM subtype-specific pathways. Our analysis was able to recover some of the …

Hp-Daemon: HIgh PErformance DIstributed ADaptive ENergy-Efficient MAtrix-MultiplicatiOn, Li Tan, Longxiang Chen, Zizhong Chen, Ziliang Zong, Rong Ge, Dong Li

Mathematics, Statistics and Computer Science Faculty Research and Publications

The demands of improving energy efficiency for high performance scientific applications arise crucially nowadays. Software-controlled hardware solutions directed by Dynamic Voltage and Frequency Scaling (DVFS) have shown their effectiveness extensively. Although DVFS is beneficial to green computing, introducing DVFS itself can incur non-negligible overhead, if there exist a large number of frequency switches issued by DVFS. In this paper, we propose a strategy to achieve the optimal energy savings for distributed matrix multiplication via algorithmically trading more computation and communication at a time adaptively with user-specified memory costs for less DVFS switches, which saves 7.5% more energy on average than …

Recurrence Relations For Moments Of Dual Generalized Order Statistics From Weibull Gamma Distribution And Its Characterizations, M. A. W. Mahmoud, Y. Abdel-Aty, N. M. Mohamed, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this paper, we establish explicit forms and new recurrence relations satisfied by the single and product moments of dual generalized order statistics from Weibull gamma distribution (WGD). The results include as particular cases the relations for moments of reversed order statistics and lower records. We present characterizations of WGD based on (i) recurrence relation for single moments, (ii) truncated moments of certain function of the variable and (iii) hazard function.

Indemics: An Interactive High-Performance Computing Framework For Data Intensive Epidemic Modeling, Keith R. Bisset, Jiangzhuo Chen, Suruchi Deodhar, Xizhou Feng, Yifei Ma, Madhav V. Marathe

Mathematics, Statistics and Computer Science Faculty Research and Publications

We describe the design and prototype implementation of Indemics (_Interactive; Epi_demic; _Simulation;)—a modeling environment utilizing high-performance computing technologies for supporting complex epidemic simulations. Indemics can support policy analysts and epidemiologists interested in planning and control of pandemics. Indemics goes beyond traditional epidemic simulations by providing a simple and powerful way to represent and analyze policy-based as well as individual-based adaptive interventions. Users can also stop the simulation at any point, assess the state of the simulated system, and add additional interventions. Indemics is available to end-users via a web-based interface.

Detailed performance analysis shows that Indemics greatly enhances the …

Efficient Detection Of Counterfeit Products In Large-Scale Rfid Systems Using Batch Authentication Protocols, Farzana Rahman, Sheikh Iqbal Ahamed

Mathematics, Statistics and Computer Science Faculty Research and Publications

RFID technology facilitates processing of product information, making it a promising technology for anti-counterfeiting. However, in large-scale RFID applications, such as supply chain, retail industry, pharmaceutical industry, total tag estimation and tag authentication are two major research issues. Though there are per-tag authentication protocols and probabilistic approaches for total tag estimation in RFID systems, the RFID authentication protocols are mainly per-tag-based where the reader authenticates one tag at each time. For a batch of tags, current RFID systems have to identify them and then authenticate each tag sequentially, one at a time. This increases the protocol execution time due to …

Remarks On A Paper Of Lee And Lim, Gholamhossein Hamedani, Michael Slattery

Mathematics, Statistics and Computer Science Faculty Research and Publications

Lee and Lim (2009) state three characterizations of Loamax, exponential and power function distributions, the proofs of which, are based on the solutions of certain second order non-linear differential equations. For these characterizations, they make the following statement : "Therefore there exists a unique solution of the differential equation that satisfies the given initial conditions". Although the general solution of their first differential equation is easily obtainable, they do not obtain the general solutions of the other two differential equations to ensure their claim via initial conditions. In this very short report, we present the general solutions of these equations …

The Transmuted Marshall-Olkin Fréchet Distribution: Properties And Applications, Ahmed Z. Afify, Gholamhossein Hamedani, Indranil Ghosh, M. E. Mead

Mathematics, Statistics and Computer Science Faculty Research and Publications

This paper introduces a new four-parameter lifetime model, which extends the Marshall-Olkin Fréchet distribution introduced by Krishna et al. (2013), called the transmuted Marshall-Olkin Fréchet distribution. Various structural properties including ordinary and incomplete moments, quantile and generating function, Rényi and q-entropies and order statistics are derived. The maximum likelihood method is used to estimate the model parameters. We illustrate the superiority of the proposed distribution over other existing distributions in the literature in modeling two real life data sets.

Characterizations Of New Modified Weibull Distribution, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Several characterizations of a New Modified Weibull distribution, introduced by Doostmoradi et al. (2014), are presented. These characterizations are based on: (i) truncated moment of a function of the random variable; (ii) the hazard function; (iii) a single function of the random variable; (iv) truncated moment of certain function of the 1st order statistic.

Varieties Of P-Restriction Semigroups, Peter R. Jones

Mathematics, Statistics and Computer Science Faculty Research and Publications

The restriction semigroups, in both their one-sided and two-sided versions, have arisen in various fashions, meriting study for their own sake. From one historical perspective, as “weakly E-ample” semigroups, the definition revolves around a “designated set” of commuting idempotents, better thought of as projections. This class includes the inverse semigroups in a natural fashion. In a recent paper, the author introduced P-restriction semigroups in order to broaden the notion of “projection” (thereby encompassing the regular *-semigroups). That study is continued here from the varietal perspective introduced for restriction semigroups by V. Gould. The relationship between varieties of regular …

Efficient And Long-Time Accurate Second-Order Methods For The Stokes-Darcy System, Wenbin Chen, Max Gunzburger, Dong Sun, Xiaoming Wan

Mathematics and Statistics Faculty Research & Creative Works

We propose and study two second order in time implicit-explicit methods for the coupled Stokes-Darcy system that governs flows in karst aquifers and other subsurface flow systems. the first method is a combination of a second-order backward differentiation formula and the second order Gear's extrapolation approach. the second is a combination of the second-order Adams-Moulton and second-order Adams-Bashforth methods. Both algorithms only require the solution of decoupled Stokes and Darcy problems at each time-step. Hence, these schemes are very efficient and can be easily implemented using legacy codes. We establish the unconditional and uniform in time stability for both schemes. …

Using Intelligent Prefetching To Reduce The Energy Consumption Of A Large-Scale Storage System, Brian Romoser, Ziliang Zong, Ribel Fares, Joal Wood, Rong Ge

Mathematics, Statistics and Computer Science Faculty Research and Publications

Many high performance large-scale storage systems will experience significant workload increases as their user base and content availability grow over time. The U.S. Geological Survey (USGS) Earth Resources Observation and Science (EROS) center hosts one such system that has recently undergone a period of rapid growth as its user population grew nearly 400% in just about three years. When administrators of these massive storage systems face the challenge of meeting the demands of an ever increasing number of requests, the easiest solution is to integrate more advanced hardware to existing systems. However, additional investment in hardware may significantly increase the …

Survival Analysis Of Cardiovascular Diseases, Yuanxin Hu

All Theses and Dissertations (ETDs)

No abstract provided.

Certain Fractional Integral Operators And The Generalized Incomplete Hypergeometric Functions, H. M. Srivastava, Praveen Agarwal

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we apply a certain general pair of operators of fractional integration involving Appell’s function F₃ in their kernel to the generalized incomplete hypergeometric functions _pΓ_q[z] and _pɣ_q [z], which were introduced and studied systematically by Srivastava et al. in the year 2012. Some interesting special cases and consequences of our main results are also considered.

The Log-Beta Generalized Half-Normal Regression Model, Rodrigo R. Pescim, Edwin M. M. Ortega, Gauss M. Cordeiro, Clarice G. B. Demtrio, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We introduce a log-linear regression model based on the beta generalized half-normal distribution (Pescim et al., 2010). We formulate and develop a log-linear model using a new distribution so-called the log-beta generalized half normal distribution. We derive expansions for the cumulative distribution and density functions which do not depend on complicated functions. We obtain formal expressions for the moments and moment generating function. We characterize the proposed distribution using a simple relationship between two truncated moments. An advantage of the new distribution is that it includes as special sub-models classical distributions reported in the lifetime literature. We also show that …

Random Search Models Of Foraging Behavior: Theory, Simulation, And Observation, Ben C. Nolting

Department of Mathematics: Dissertations, Theses, and Student Research

Many organisms, from bacteria to primates, use stochastic movement patterns to find food. These movement patterns, known as search strategies, have recently be- come a focus of ecologists interested in identifying universal properties of optimal foraging behavior. In this dissertation, I describe three contributions to this field. First, I propose a way to extend Charnov's Marginal Value Theorem to the spatially explicit framework of stochastic search strategies. Next, I describe simulations that compare the efficiencies of sensory and memory-based composite search strategies, which involve switching between different behavioral modes. Finally, I explain a new behavioral analysis protocol for identifying the …

Road Systems And Betweenness, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

A road system is a collection of subsets of a set—the roads—such that every singleton subset is a road in the system and every doubleton subset is contained in a road. The induced ternary (betweenness) relation is defined by saying that a point c lies between points a and b if c is an element of every road that contains both a and b . Traditionally, betweenness relations have arisen from a plethora of other structures on a given set, reflecting intuitions that range from the order-theoretic to the geometric and topological. In this paper we initiate a study …

Progressive Reliability Method And Its Application To Offshore Mooring Systems, Mir Emad Mousavi, Paolo Gardoni, Mehdi Maadooliat

Mathematics, Statistics and Computer Science Faculty Research and Publications

Assessing the reliability of complex systems (e.g. structures) is essential for a reliability-based optimal design that balances safety and costs of such systems. This paper proposes the Progressive Reliability Method (PRM) for the quantification of the reliability of complex systems. The proposed method is a closed-form solution for calculating the probability of failure. The new method is flexible to the definition of “failure” (i.e., can consider serviceability and ultimate-strength failures) and uses the rules of probability theory to estimate the failure probability of the system or its components. The method is first discussed in general and then illustrated in two …

Assessing Protein Conformational Sampling Methods Based On Bivariate Lag-Distributions Of Backbone Angles, Mehdi Maadooliat, Xin Gao, Jianhua Z. Huang

Mathematics, Statistics and Computer Science Faculty Research and Publications

Despite considerable progress in the past decades, protein structure prediction remains one of the major unsolved problems in computational biology. Angular-sampling-based methods have been extensively studied recently due to their ability to capture the continuous conformational space of protein structures. The literature has focused on using a variety of parametric models of the sequential dependencies between angle pairs along the protein chains. In this article, we present a thorough review of angular-sampling-based methods by assessing three main questions: What is the best distribution type to model the protein angles? What is a reasonable number of components in a mixture model …

Mathematical Engineering And Control With Applications, Mamdouh M. El Kady, Martin Bohner, J. Liang, Mouffak Benchohra

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

The Kalman Filter For Linear Systems On Time Scales, Martin Bohner, Nick Wintz

Mathematics and Statistics Faculty Research & Creative Works

We introduce the Kalman filter for linear systems on time scales, which includes the discrete and continuous versions as special cases. When the system is also stochastic, we show that the Kalman filter is an observer that estimates the system when the state is corrupted by noisy measurements. Finally, we show that the duality of the Kalman filter and the Linear Quadratic Regulator (LQR) is preserved in their unification on time scales. A numerical example is provided. © 2013 Elsevier Ltd.

Minkowski And Beckenbach-Dresher Inequalities And Functionals On Time Scales, Rabia Bibi, Martin Bohner, Josip Pečarić, Sanja Varǒsanec

Mathematics and Statistics Faculty Research & Creative Works

We obtain integral forms of the Minkowski inequality and Beckenbach-Dresher inequality on time scales. Also, we investigate a converse of Minkowski's inequality and several functionals arising from the Minkowski inequality and the Beckenbach-Dresher inequality. © ELEMENT, Zagreb.

A Jackknife Empirical Likelihood Approach To Goodness Of Fit U-Statistic Testing With Side Information, Qun Lin

Open Access Dissertations

Motivated by applications to goodness of fit U-statistics testing, the jackknife empirical likelihood of Jing, et al. (2009) is justified with an alternative approach, and the Wilks theorem for vector U-statistics is proved. This generalizes Owen's empirical likelihood theorem for a vector mean to a vector U-statistics-based mean and includes the jackknife empirical likelihood of U-statistics with side information as a special case. The results are generalized to allow for the constraints to use estimated criteria functions and for the number of constraints to grow with the sample size. The latter is needed to handle naturally occurring nuisance parameters in …

Characterizations Of Distribution Of Ratio Of Rayleigh Random Variables, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Various characterizations of the distribution of the ratio of two independent Rayleigh random variables are presented. These characterizations are based, on a truncated moment; on hazard function; and on certain functions of order statistics.