Statistics and Probability Commons^™

A Note On Sum, Difference, Product And Ratio Of Kumaraswamy Random Variables, Avishek Mallick, Indranil Ghosh, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Explicit expressions for the densities of S = X₁ + X₂ , D = X₁ − X₂ , P = X₁X₂ and R= X₁/X₂ are derived when X₁ and X₂ are independent or sub-independent Kumaraswamy random variables. The expressions appear to involve the incomplete gamma functions. Some possible real life scenarios are mentioned in which such quantities might be of interest.

Hierarchical Bayesian Data Fusion Using Autoencoders, Yevgeniy Vladimirovich Reznichenko

Master's Theses (2009 -)

In this thesis, a novel method for tracker fusion is proposed and evaluated for vision-based tracking. This work combines three distinct popular techniques into a recursive Bayesian estimation algorithm. First, semi supervised learning approaches are used to partition data and to train a deep neural network that is capable of capturing normal visual tracking operation and is able to detect anomalous data. We compare various methods by examining their respective receiver operating conditions (ROC) curves, which represent the trade off between specificity and sensitivity for various detection threshold levels. Next, we incorporate the trained neural networks into an existing data …

Robust Computation In 2d Absolute Eit (A-Eit) Using D-Bar Methods With The “Exp” Approximation, Sarah J. Hamilton, J. L. Mueller, T. R. Santos

Mathematical and Statistical Science Faculty Research and Publications

Objective

Absolute images have important applications in medical Electrical Impedance Tomography (EIT) imaging, but the traditional minimization and statistical based computations are very sensitive to modeling errors and noise. In this paper, it is demonstrated that D-bar reconstruction methods for absolute EIT are robust to such errors.

Approach

The effects of errors in domain shape and electrode placement on absolute images computed with 2-D D-bar reconstruction algorithms are studied on experimental data.

Main Results

It is demonstrated with tank data from several EIT systems that these methods are quite robust to such modeling errors, and furthermore the artefacts arising from …

Combinatorial Proofs Of Identities Of Alzer And Prodinger And Some Generalizations, John Engbers, Christopher Stocker

Mathematics, Statistics and Computer Science Faculty Research and Publications

We provide combinatorial proofs of identities published by Alzer and Prodinger. These identities include that for integers b, n, and r with b ≥ 1 and n − 1 ≥ r ≥ 0 we have

and for integers b, n, and r with b ≥ 0 and n − 1 ≥ r ≥ 0 we have

Our combinatorial proofs generalize squares to sth powers, and involve generalized Eulerian numbers and generalized Delannoy numbers.

Dynamic Statistical Models For Pyroclastic Density Current Generation At Soufrière Hills Volcano, Robert L. Wolpert, Elaine T. Spiller, Eliza S. Calder

Mathematics, Statistics and Computer Science Faculty Research and Publications

To mitigate volcanic hazards from pyroclastic density currents, volcanologists generate hazard maps that provide long-term forecasts of areas of potential impact. Several recent efforts in the field develop new statistical methods for application of flow models to generate fully probabilistic hazard maps that both account for, and quantify, uncertainty. However, a limitation to the use of most statistical hazard models, and a key source of uncertainty within them, is the time-averaged nature of the datasets by which the volcanic activity is statistically characterized. Where the level, or directionality, of volcanic activity frequently changes, e.g., during protracted eruptive episodes, or at …

Impacts Of Simultaneous Multislice Acquisition On Sensitivity And Specificity In Fmri, Benjamin B. Risk, Mary C. Kociuba, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

Simultaneous multislice (SMS) imaging can be used to decrease the time between acquisition of fMRI volumes, which can increase sensitivity by facilitating the removal of higher-frequency artifacts and boosting effective sample size. The technique requires an additional processing step in which the slices are separated, or unaliased, to recover the whole brain volume. However, this may result in signal “leakage” between aliased locations, i.e., slice “leakage,” and lead to spurious activation (decreased specificity). SMS can also lead to noise amplification, which can reduce the benefits of decreased repetition time. In this study, we evaluate the original slice-GRAPPA (no leak block) …

The Kumaraswamy Marshall-Olkin Log-Logistic Distribution With Application, Selen Cakmakyapan, Gamze Ozel, Yehia Mousa Hussein El Gebaly, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this paper, we define and study a new lifetime model called the Kumaraswamy Marshall-Olkin log-logistic distribution. The new model has the advantage of being capable of modeling various shapes of aging and failure criteria. The new model contains some well-known distributions as special cases such as the Marshall-Olkin log-logistic, log-logistic, lomax, Pareto type II and Burr XII distributions. Some of its mathematical properties including explicit expressions for the quantile and generating functions, ordinary moments, skewness, kurtosis are derived. The maximum likelihood estimators of the unknown parameters are obtained. The importance and flexibility of the new model is proved empirically …

Preservice Mathematics Teachers' Conceptions And Enactments Of Modeling Standards, Hyunyi Jung, Jill Newton

Mathematics, Statistics and Computer Science Faculty Research and Publications

Mathematical modeling has been highlighted recently as Common Core State Standards for Mathematics [CCSSM] included Model with Mathematics as one of the Standards for Mathematical Practices [SMP] and a modeling strand in the high school standards. This common aspect of standards across most states in the U.S. intended by CCSSM authors and policy makers seems to mitigate the diverse notions of mathematical modeling. When we observed secondary mathematics preservice teachers [PSTs] who learned about the SMP and used CCSSM modeling standards to plan and enact lessons, however, we noted differences in their interpretations and enactments of the standards, despite their …

Characterizations And Infinite Divisibility Of Certain Recently Introduced Distributions Iv, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Certain characterizations of recently proposed univariate continuous distributions are presented in different directions. This work contains a good number of reintroduced distributions and may serve as a source of preventing the reinvention and/or duplication of the existing distributions in the future.

Supporting Accurate Interpretation Of Self-Administered Medical Test Results For Mobile Health: Assessment Of Design, Demographics, And Health Condition, Jess C. Hohenstein, Eric P.S. Baumer, Lindsay Reynolds, Elizabeth L. Murnane, Dakota O'Dell, Seoho Lee, Shion Guha, Yu Qi, Erin Rieger, Geri K. Gay

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background: Technological advances in personal informatics allow people to track their own health in a variety of ways, representing a dramatic change in individuals’ control of their own wellness. However, research regarding patient interpretation of traditional medical tests highlights the risks in making complex medical data available to a general audience.

Objective: This study aimed to explore how people interpret medical test results, examined in the context of a mobile blood testing system developed to enable self-care and health management.

Methods: In a preliminary investigation and main study, we presented 27 and 303 adults, respectively, with hypothetical results from several …

A Patient-Specific Treatment Model For Graves’ Hyperthyroidism, Balamurugan Pandiyan, Stephen J. Merrill, Flavia Di Bari, Alessandro Antonelli, Salvatore Benvenga

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background: Graves’ is disease an autoimmune disorder of the thyroid gland caused by circulating anti-thyroid receptor antibodies (TRAb) in the serum. TRAb mimics the action of thyroid stimulating hormone (TSH) and stimulates the thyroid hormone receptor (TSHR), which results in hyperthyroidism (overactive thyroid gland) and goiter. Methimazole (MMI) is used for hyperthyroidism treatment for patients with Graves’ disease.

Methods: We have developed a model using a system of ordinary differential equations for hyperthyroidism treatment with MMI. The model has four state variables, namely concentration of MMI (in mg/L), concentration of free thyroxine - FT4 (in pg/mL), and concentration of TRAb …

Regrets, I'Ve Had A Few: When Regretful Experiences Do (And Don't) Compel Users To Leave Facebook, Shion Guha, Eric P.S. Baumer, Geri K. Gay

Mathematics, Statistics and Computer Science Faculty Research and Publications

Previous work has explored regretful experiences on social media. In parallel, scholars have examined how people do not use social media. This paper aims to synthesize these two research areas and asks: Do regretful experiences on social media influence people to (consider) not using social media? How might this influence differ for different sorts of regretful experiences? We adopted a mixed methods approach, combining topic modeling, logistic regressions, and contingency analysis to analyze data from a web survey with a demographically representative sample of US internet users (n=515) focusing on their Facebook use. We found that experiences that arise because …

Type I General Exponential Class Of Distributions, Gholamhossein G. Hamedani, Haitham M. Yousof, Mahdi Rasekhi, Morad Alizadeh, Seyed Morteza Najibi

Mathematics, Statistics and Computer Science Faculty Research and Publications

We introduce a new family of continuous distributions and study the mathematical properties of the new family. Some useful characterizations based on the ratio of two truncated moments and hazard function are also presented. We estimate the model parameters by the maximum likelihood method and assess its performance based on biases and mean squared errors in a simulation study framework.

On Comparability Of Bigrassmannian Permutations, John Engbers, Adam Hammett

Mathematics, Statistics and Computer Science Faculty Research and Publications

Let S_n and G_n denote the respective sets of ordinary and bigrassmannian (BG) permutations of order n, and let (G_n,≤) denote the Bruhat ordering permutation poset. We study the restricted poset (B_n,≤), first providing a simple criterion for comparability. This criterion is used to show that that the poset is connected, to enumerate the saturated chains between elements, and to enumerate the number of maximal elements below r fixed elements. It also quickly produces formulas for β(ω) (α(ω), respectively), the number of BG permutations weakly below (weakly above, respectively) a fixed ω ∈ B …

On The Mixtures Of Weibull And Pareto (Iv) Distribution: An Alternative To Pareto Distribution, I. Ghosh, Gholamhossein G. Hamedani, Naveen K. Bansal, Mehdi Maadooliat

Mathematics, Statistics and Computer Science Faculty Research and Publications

Finite mixture models have provided a reasonable tool to model various types of observed phenomena, specially those which are random in nature. In this article, a finite mixture of Weibull and Pareto (IV) distribution is considered and studied. Some structural properties of the resulting model are discussed including estimation of the model parameters via expectation maximization (EM) algorithm. A real-life data application exhibits the fact that in certain situations, this mixture model might be a better alternative than the rival popular models.

On Characterizations Of Mcllog, Ellogw, Pthl And K-Ge Distributions, Gholamhossein G. Hamedani, Nadeem Shafique Butt

Mathematics, Statistics and Computer Science Faculty Research and Publications

Huang S. and Oluyede (2016), Oluyede et al. (2016), Krishnarani (2016) and Rather and Rather (2017) consider the "McDonald Log-Logistic", the "Exponentiated Log-Logistic Weibull", the "Power Transformation Half-Logistic" and "k-Generalized Exponential" distributions, respectively, and study certain properties and applications of these distributions. The present short note is intended to complete, in some way, the above mentioned works via establishing certain characterizations of these distributions in different directions.

Characterizations And Infinite Divisibility Of Certain Recently Introduced Distributions Iii, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Certain characterizations of recently proposed univariate continuous distributions are presented in different directions. This work may be a source of preventing reinventing and duplicating the existing distributions and calling them newly proposed distributions.

A Bayesian Variable Selection Approach Yields Improved Detection Of Brain Activation From Complex-Valued Fmri, Cheng-Han Yu, Raquel Prado, Hernando Ombao, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

Voxel functional magnetic resonance imaging (fMRI) time courses are complex-valued signals giving rise to magnitude and phase data. Nevertheless, most studies use only the magnitude signals and thus discard half of the data that could potentially contain important information. Methods that make use of complex-valued fMRI (CV-fMRI) data have been shown to lead to superior power in detecting active voxels when compared to magnitude-only methods, particularly for small signal-to-noise ratios (SNRs). We present a new Bayesian variable selection approach for detecting brain activation at the voxel level from CV-fMRI data. We develop models with complex-valued spike-and-slab priors on the activation …

The Kumaraswamy Weibull Geometric Distribution With Applications, Mahdi Rasekhi, Morad Alizadeh, Gholamhossein G. Hamedani

Mathematical and Statistical Science Faculty Research and Publications

In this work, we study the kumaraswamy weibull geometric (Kw-WG) distribution which includes as special cases, several models such as the kumaraswamy weibull distribution, kumaraswamy exponential distribution, weibull geometric distribution, exponential geometric distribution, to name a few. This distribution was monotone and non-monotone hazard rate functions, which are useful in lifetime data analysis and reliability. We derive some basic properties of the Kw-WG distribution including non-central rth-moments, skewness, kurtosis, generating functions, mean deviations, mean residual life, entropy, order statistics and certain characterizations of our distribution. The method of maximum likelihood is used for estimating the model parameters and a simulation …

Complex-Valued Time Series Modeling For Improved Activation Detection In Fmri Studies, Daniel W. Adrian, Ranjan Maitra, Daniel B. Rowe

Mathematical and Statistical Science Faculty Research and Publications

A complex-valued data-based model with th order autoregressive errors and general real/imaginary error covariance structure is proposed as an alternative to the commonly used magnitude-only data-based autoregressive model for fMRI time series. Likelihood-ratio-test-based activation statistics are derived for both models and compared for experimental and simulated data. For a dataset from a right-hand finger-tapping experiment, the activation map obtained using complex-valued modeling more clearly identifies the primary activation region (left functional central sulcus) than the magnitude-only model. Such improved accuracy in mapping the left functional central sulcus has important implications in neurosurgical planning for tumor and epilepsy patients. Additionally, we …

On Extended Quadratic Hazard Rate Distribution: Development, Properties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein G. Hamedani, Wenhui Sheng, Munir Ahmad

Mathematical and Statistical Science Faculty Research and Publications

In this paper, we propose a flexible extended quadratic hazard rate (EQHR) distribution with increasing, decreasing, bathtub and upside-down bathtub hazard rate function. The EQHR density is arc, right-skewed and symmetrical shaped. This distribution is also obtained from compounding mixture distributions. Stochastic orderings, descriptive measures on the basis of quantiles, order statistics and reliability measures are theoretically established. Characterizations of the EQHR distribution are studied via different techniques. Parameters of the EQHR distribution are estimated using the maximum likelihood method. Goodness of fit of this distribution through different methods is studied.

On Modified Burr Xii-Inverse Exponential Distribution: Prop¬Erties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein Hamedani, Haitham M. Yousof, Azeem Ali, Munir Ahmad

Mathematical and Statistical Science Faculty Research and Publications

In this paper, a flexible lifetime distribution with increasing, increasing and decreasing and modified bathtub hazard rate called Modified Burr XII-Inverse Exponential (MBXII-IE) is introduced. The density function of MBXII-IE has exponential, left-skewed, right-skewed and symmetrical shapes. Descriptive measures such as moments, moments of order statistics, incomplete moments, inequality measures, residual life function and reliability measures are theoretically established. The MBXII-IE distribution is characterized via different techniques. Parameters of MBXII-IE distribution are estimated using maximum likelihood method. The simulation study is performed to illustrate the performance of the Maximum Likelihood Estimates (MLEs) of the parameters of the MBXII-IE distribution. The …

Interproximal Distance Analysis Of Stereolithographic Casts Made By Cad-Cam Technology: An In Vitro Study, Melanie Hoffman, Seok-Hwan Cho, Naveen K. Bansal

Mathematics, Statistics and Computer Science Faculty Research and Publications

Statement of problem

The accuracy of interproximal distances of the definitive casts made by computer-aided design and computer-aided manufacturing (CAD-CAM) technology is not yet known.

Purpose

The purpose of this in vitro study was to compare the interproximal distances of stereolithographic casts made by CAD-CAM technology with those of stone casts made by the conventional method.

Material and methods

Dentoform teeth were prepared for a single ceramic crown on the maxillary left central incisor, a 3-unit fixed dental prosthesis (FDP) on the second premolar for a metal-ceramic crown, and a maxillary right first molar for a metal crown. Twenty digital …

Dodrant-Homomorphic Encryption For Cloud Databases Using Table Lookup, Thomas Schwarz

Mathematics, Statistics and Computer Science Faculty Research and Publications

Users of large commercial databases increasingly want to outsource their database operations to a cloud service providers, but guaranteeing the privacy of data in an outsourced database has become the major obstacle to this move. Encrypting all data solves the privacy issue, but makes many operations on the data impossible in the cloud, unless the service provider has the capacity to decrypt data temporarily. Homomorphic encryption would solve this issue, but despite great and on-going progress, it is still far from being operationally feasible. In 2015, we presented what we now call dodrant-homomorphic encryption, a method that encrypts numeric values …

The Double-Edged Sword: A Mixed Methods Study Of The Interplay Between Bipolar Disorder And Technology Use, Mark Matthews, Elizabeth Murnane, Jaime Snyder, Shion Guha, Pamara Chang, Gavin Doherty, Geri K. Gay

Mathematics, Statistics and Computer Science Faculty Research and Publications

Human behavior is increasingly reflected or acted out through technology. This is of particular salience when it comes to changes in behavior associated with serious mental illnesses including schizophrenia and bipolar disorder. Early detection is crucial for these conditions but presently very challenging to achieve. Potentially, characteristics of these conditions' traits and symptoms, at both idiosyncratic and collective levels, may be detectable through technology use patterns. In bipolar disorder specifically, initial evidence associates changes in mood with changes in technology-mediated communication patterns. However much less is known about how people with bipolar disorder use technology more generally in their lives, …

On Congruence Lattices Of Nilsemigroups, Alexander L. Popovich, Peter R. Jones

Mathematics, Statistics and Computer Science Faculty Research and Publications

We prove that the congruence lattice of a nilsemigroup is modular if and only if the width of the semigroup, as a poset, is at most two, and distributive if and only if its width is one. In the latter case, such semigroups therefore coincide with the nil Δ">Δ Δ -semigroups. It is further shown that if a finitely generated nilsemigroup has modular congruence lattice, then the semigroup is finite.

Implant Treatment In The Predoctoral Clinic: A Retrospective Database Study Of 1091 Patients, Soni Prasad, Christopher Hambrook, Eric Reigle, Katherine Sherman, Naveen K. Bansal, Arthur F. Hefti

Mathematics, Statistics and Computer Science Faculty Research and Publications

Purpose: This retrospective study was conducted at the Marquette University School of Dentistry to (1) characterize the implant patient population in a predoctoral clinic, (2) describe the implants inserted, and (3) provide information on implant failures.

Materials and Methods: The study cohort included 1091 patients who received 1918 dental implants between 2004 and 2012, and had their implants restored by a crown or a fixed dental prosthesis. Data were collected from patient records, entered in a database, and summarized in tables and figures. Contingency tables were prepared and analyzed by a chi-squared test. The cumulative survival probability of implants was …

Merging Peg Solitaire In Graphs, John Engbers, Ryan Weber

Mathematics, Statistics and Computer Science Faculty Research and Publications

Peg solitaire has recently been generalized to graphs. Here, pegs start on all but one of the vertices in a graph. A move takes pegs on adjacent vertices x and y, with y also adjacent to a hole on vertex z, and jumps the peg on x over the peg ony to z, removing the peg on y. The goal of the game is to reduce the number of pegs to one.

We introduce the game merging peg solitaire on graphs, where a move takes pegs on vertices x and z (with a hole on y) and merges them to …

A Perspective On The Challenges And Issues In Developing Biomarkers For Human Allergic Risk Assessments, Ying Mu, Dianne E. Godar, Stephen Merrill

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

A Privacy Preserving Framework For Rfid Based Healthcare Systems, Farzana Rahman, Anwarul A. Bhuiyan, Sheikh Iqbal Ahamed

Mathematics, Statistics and Computer Science Faculty Research and Publications

RFID (Radio Frequency IDentification) is anticipated to be a core technology that will be used in many practical applications of our life in near future. It has received considerable attention within the healthcare for almost a decade now. The technology’s promise to efficiently track hospital supplies, medical equipment, medications and patients is an attractive proposition to the healthcare industry. However, the prospect of wide spread use of RFID tags in the healthcare area has also triggered discussions regarding privacy, particularly because RFID data in transit may easily be intercepted and can be send to track its user (owner). In a …