Mathematics Commons^™

Characterizations Of Marshall-Olkin Discrete Reduced Modified Weibull Distribution, Gholamhossein G. Hamedani

Mathematical and Statistical Science Faculty Research and Publications

Characterizing a distribution is an important problem in applied sciences, where an investigator is vitally interested to know if their model follows the right distribution. To this end, the investigator relies on conditions under which their model would follow specifically chosen distribution. Certain characterizations of the Marshall-Olkin discrete reduced modified Weibull distribution are presented to complete, in some way, their work.

The Extended Alpha Power Transformed Family Of Distributions: Properties And Applications, Zubair Ahmad, Muhammad Ilyas, Gholamhossein G. Hamedani

Mathematical and Statistical Science Faculty Research and Publications

In this article, a new family of lifetime distributions by adding an additional parameter to the existing distributions is introduced. The new family is called, the extended alpha power transformed family of distributions. For the proposed family, explicit expressions for some mathematical properties along with estimation of parameters through Maximum likelihood Method are discussed. A special sub-model, called the extended alpha power transformed Weibull distribution is considered in detail. The proposed model is very flexible and can be used to model data with increasing, decreasing or bathtub shaped hazard rates. To access the behavior of the model parameters, a small …

On The Generalized Log Burr Iii Distribution: Development, Properties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein Hamedani, Azeem Ali, Munir Ahmad

Mathematical and Statistical Science Faculty Research and Publications

In this paper, we present a generalized log Burr III (GLBIII) distribution developed on the basis of a generalized log Pearson differential equation (GLPE). The density function of the GLBIII is exponential, arc, J, reverse-J, bimodal, left-skewed, right- skewed and symmetrical shaped. The hazard rate function of GLBIII distribution has various shapes such as constant, increasing, decreasing, increasing-decreasing, upside- down bathtub and modified bathtub. Descriptive measures such as quantile function, sub- models, ordinary moments, moments of order statistics, incomplete moments, reliability and uncertainty measures are theoretically established. The GLBIII distribution is characterized via different techniques. Parameters of the GLBIII distribution …

Mental Imagery Practice As A Therapy For Naming Impairments: A Preliminary Study, Subhash Bhatnagar, Bridget Patek, Yasmeen Khan-Ansari, Naveen K. Bansal, Hugh Buckingham, Lotfi Hacein-Bey

Speech Pathology and Audiology Faculty Research and Publications

Background

Anomia remains one of the most recalcitrant linguistic disruptions in aphasia to treat. Developing successful interventions to address the word-finding deficits are complicated by the post-stroke symptom variability and inconsistent recovery patterns associated with anomia. Most of the current treatment methods, with a focus on specific compensating techniques and the repetitive practice of a limited set of items, have had variable success in naming treatment. However, it has not been possible to predict the gains in generalizing the learning beyond the stimuli used in practice or the controlled clinical setting. In this preliminary case study, we explore the value …

On Burr Iii-Pareto Distribution: Development, Properties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein G. Hamedani, Mustafa Ç. Korkmaz, Munir Ahmad

Mathematical and Statistical Science Faculty Research and Publications

In this paper, a new four parameter lifetime model with increasing, decreasing, increasing-decreasing, decreasing-increasing-decreasing, modified bathtub, bathtub and inverted bathtub hazard rate function called Burr III-Pareto (BIII-Pareto) is developed on the basis of the T-X family technique. The BIII-Pareto density function is arc, J-shape, reverse J-shape, positively, negatively skewed and symmetrical. Some structural and mathematical properties including moments, moments of order statistics, inequality measures and reliability measures are theoretically established. The BIII-Pareto distribution is characterized via different techniques. Parameters of the BIII-Pareto distribution are estimated using maximum likelihood method. The simulation study for performance of the maximum likelihood estimates (MLEs) …

Mathematical Modeling And Classroom Discourse: A Case For Modeling-Specific Discussion Strategies, Ashley Dorlack, Hyunyi Jung, Sarah Brand, Samuel Franklin Gailliot

Mathematical and Statistical Science Faculty Research and Publications

No abstract provided.

Mathematical Modeling Experiences: Narratives From A Preservice Teacher And An Instructor, Sarah Brand, Hyunyi Jung

Mathematical and Statistical Science Faculty Research and Publications

Regardless of the benefits of engaging in mathematical modeling, few preservice teachers (PTs) have experienced mathematical modeling firsthand. This study offers an example of how to make sense of the interaction between the teaching and learning of mathematical modeling by examining a teacher educator’s decision making, her analysis of 36 PTs’ learning, and an in-depth narrative from a PT. Findings show the value of engaging with structurally relevant mathematical modeling tasks and considering social issues via mathematical modeling, resulting in task designs which aim to deepen students’ understanding of society and mathematics.

A New Extension Of Lindley Distribution: Modified Validation Test, Characterizations And Different Methods Of Estimation, Mohamed Ibrahim, Abhimanyu Singh Yadav, Haitham M. Yousof, Hafida Goual, Gholamhossein Hamedani

Mathematical and Statistical Science Faculty Research and Publications

In this paper, a new extension of Lindley distribution has been introduced. Certain characterizations based on truncated moments, hazard and reverse hazard function, conditional expectation of the proposed distribution are presented. Besides, these characterizations, other statistical/mathematical properties of the proposed model are also discussed. The estimation of the parameters is performed through different classical methods of estimation. Bayes estimation is computed under gamma informative prior under the squared error loss function. The performances of all estimation methods are studied via Monte Carlo simulations in mean square error sense. The potential of the proposed model is analyzed through two data sets. …

On The Modified Burr Xii-Power Distribution: Development, Properties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein G. Hamedani, Mustafa Ç. Korkmaz, Munir Ahmad

Mathematical and Statistical Science Faculty Research and Publications

In this paper, a flexible lifetime distribution with increasing, decreasing and bathtub hazard rate called the Modified Burr XII-Power (MBXII-Power) is developed on the basis of the T-X family technique. The density function of the MBXII-Power is arc, exponential, left-skewed, right-skewed, J, reverse-J and symmetrical shaped. Descriptive measures such as moments, moments of order statistics, incomplete moments, inequality measures, residual life functions and reliability measures are theoretically established. The MBXII-Power distribution is characterized via different techniques. Parameters of the MBXII-Power distribution are estimated using maximum likelihood method. The simulation study is performed on the basis of graphical results to see …

Characterizations Of Certain Recently Introduced Discrete Distributions, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Characterizations of certain recently introduced discrete distributions are presented to complete, in some way, the works cited in the References.

On Burr Iii Marshal Olkin Family: Development, Properties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein G. Hamedani, Mustafa Ç. Korkmaz, Gauss M. Cordeiro, Haitham M. Yousof, Munir Ahmad

Mathematical and Statistical Science Faculty Research and Publications

In this paper, a flexible family of distributions with unimodel, bimodal, increasing, increasing and decreasing, inverted bathtub and modified bathtub hazard rate called Burr III-Marshal Olkin-G (BIIIMO-G) family is developed on the basis of the T-X family technique. The density function of the BIIIMO-G family is arc, exponential, left- skewed, right-skewed and symmetrical shaped. Descriptive measures such as quantiles, moments, incomplete moments, inequality measures and reliability measures are theoretically established. The BIIIMO-G family is characterized via different techniques. Parameters of the BIIIMO-G family are estimated using maximum likelihood method. A simulation study is performed to illustrate the performance of the …

The Exponentiated Generalized Topp Leone-G Family Of Distributions: Properties And Applications, Hesham Mohammed Reyad, Morad Alizadeh, Farrukh Jamal, Soha Othman, Gholamhossein G. Hamedani

Mathematical and Statistical Science Faculty Research and Publications

In this paper, we propose a new class of continuous distributions called the exponentiated generalized Topp Leone-G family that extends the Topp Leone-G family introduced by Al-Shomrani et al. (2016). We derive explicit expressions for certain mathematical properties of the new family such as; ordinary and incomplete moments, generating functions, reliability analysis, Lorenz and Bonferroni curves, Rényi entropy, stress strength model, moment of residual and reversed residual life, order statistics, extreme values and characterizations. We discuss the maximum likelihood estimates and the observed information matrix for the model parameters. Two real data sets are used to illustrate the flexibility of …

Group Presentations As A Site For Collective Modeling Activity, Corey Brady, Hyunyi Jung

Mathematical and Statistical Science Faculty Research and Publications

We approach student presentations of solutions to modeling tasks as occasions for whole-class reflection on the rich conceptual work that small-group teams have done in parallel. Analyzing and interpreting these interactions can offer insights into how a classroom group negotiates a shared sense of what they have learned and what they collectively view as “newsworthy” across groups from their recent (and ongoing) model-building. We describe analytical tools to interpret a classroom’s work during presentations, and we illustrate their use in a single case. This work offers a foothold for design-based research to harness presentations to improve learning, drive instructional decisions, …

The Nested Joint Clustering Via Dirichlet Process Mixture Model, Shengtong Han, Hongmei Zhang, Wenhui Sheng, Hasan Arshad

Mathematical and Statistical Science Faculty Research and Publications

This article focuses on the clustering problem based on Dirichlet process (DP) mixtures. To model both time invariant and temporal patterns, different from other existing clustering methods, the proposed semi-parametric model is flexible in that both the common and unique patterns are taken into account simultaneously. Furthermore, by jointly clustering subjects and the associated variables, the intrinsic complex shared patterns among subjects and among variables are expected to be captured. The number of clusters and cluster assignments are directly inferred with the use of DP. Simulation studies illustrate the effectiveness of the proposed method. An application to wheal size data …

Nonparametric Collective Spectral Density Estimation With An Application To Clustering The Brain Signals, Mehdi Maadooliat, Ying Sun, Tianbo Chen

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this paper, we develop a method for the simultaneous estimation of spectral density functions (SDFs) for a collection of stationary time series that share some common features. Due to the similarities among the SDFs, the log‐SDF can be represented using a common set of basis functions. The basis shared by the collection of the log‐SDFs is estimated as a low‐dimensional manifold of a large space spanned by a prespecified rich basis. A collective estimation approach pools information and borrows strength across the SDFs to achieve better estimation efficiency. Moreover, each estimated spectral density has a concise representation using the …

Smartphone-Based Prenatal Education For Parents With Preterm Birth Risk Factors, U. Olivia Kim, K. Barnekow, Sheikh Iqbal Ahamed, S. Dreier, C. Jones, M. Taylor, Md Kamrul Hasan, M. A. Basir

Mathematics, Statistics and Computer Science Faculty Research and Publications

Objective

To develop an educational mobile application (app) for expectant parents diagnosed with risk factors for premature birth.

Methods

Parent and medical advisory panels delineated the vision for the app. The app helps prepare for preterm birth. For pilot testing, obstetricians offered the app between 18–22 weeks gestational age to English speaking parents with risk factors for preterm birth. After 4 weeks of use, each participant completed a questionnaire. The software tracked topics accessed and duration of use.

Results

For pilot testing, 31 participants were recruited and 28 completed the questionnaire. After app utilization, participants reported heightened awareness of preterm …

Semicontinuity Of Betweenness Functions, Paul Bankston, Aisling Mccluskey, Richard J. Smith

Mathematics, Statistics and Computer Science Faculty Research and Publications

A ternary relational structure〈X,[⋅,⋅,⋅]〉, interpreting a notion of betweenness, gives rise to the family of intervals, with interval [a,b] being defined as the set of elements of X between a and b. Under very reasonable circumstances, X is also equipped with some topological structure, in such a way that each interval is a closed nonempty subset of X. The question then arises as to the continuity behavior—within the hyperspace context—of the betweenness function {x,y}↦[x,y]. We investigate two broad scenarios: the first involves metric spaces and Menger's betweenness interpretation; the second deals with continua and the subcontinuum interpretation.

The Transmuted Geometric-Quadratic Hazard Rate Distribution: Development, Properties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein Hamedani, Mustafa Ç. Korkmaz, Munir Ahmad

Mathematics, Statistics and Computer Science Faculty Research and Publications

We propose a five parameter transmuted geometric quadratic hazard rate (TG-QHR) distribution derived from mixture of quadratic hazard rate (QHR), geometric and transmuted distributions via the application of transmuted geometric-G (TG-G) family of Afify et al.(Pak J Statist 32(2), 139-160, 2016). Some of its structural properties are studied. Moments, incomplete moments, inequality measures, residual life functions and some other properties are theoretically taken up. The TG-QHR distribution is characterized via different techniques. Estimates of the parameters for TG-QHR distribution are obtained using maximum likelihood method. The simulation studies are performed on the basis of graphical results to illustrate the performance …

Empirical Bayesian Approach To Testing Multiple Hypotheses With Separate Priors For Left And Right Alternatives, Naveen K. Bansal, Mehdi Maadooliat, Steven J. Schrodi

Mathematics, Statistics and Computer Science Faculty Research and Publications

We consider a multiple hypotheses problem with directional alternatives in a decision theoretic framework. We obtain an empirical Bayes rule subject to a constraint on mixed directional false discovery rate (mdFDR≤α) under the semiparametric setting where the distribution of the test statistic is parametric, but the prior distribution is nonparametric. We proposed separate priors for the left tail and right tail alternatives as it may be required for many applications. The proposed Bayes rule is compared through simulation against rules proposed by Benjamini and Yekutieli and Efron. We illustrate the proposed methodology for two sets of …

Cancerin: A Computational Pipeline To Infer Cancer-Associated Cerna Interaction Networks, Duc Do, Serdar Bozdag

Mathematics, Statistics and Computer Science Faculty Research and Publications

MicroRNAs (miRNAs) inhibit expression of target genes by binding to their RNA transcripts. It has been recently shown that RNA transcripts targeted by the same miRNA could “compete” for the miRNA molecules and thereby indirectly regulate each other. Experimental evidence has suggested that the aberration of such miRNA-mediated interaction between RNAs—called competing endogenous RNA (ceRNA) interaction—can play important roles in tumorigenesis. Given the difficulty of deciphering context-specific miRNA binding, and the existence of various gene regulatory factors such as DNA methylation and copy number alteration, inferring context-specific ceRNA interactions accurately is a computationally challenging task. Here we propose a computational …

Reality Versus Grant Application Research “Plans”, Linda Burhansstipanov, Linda U. Krebs, Daniel Petereit, Mark Dignan, Sheikh Iqbal Ahamed, Michele Sargent, Krisin Cina, Kimberly Crawford, Doris Thibeault, Simone Bordeaux, Shalini Kanekar, Golam Mushih Tanimul Ahsan, Drew Williams, Ivor D. Addo

Mathematics, Statistics and Computer Science Faculty Research and Publications

This article describes the implementation of the American Indian mHealth Smoking Dependence Study focusing on the differences between what was written in the grant application compared to what happened in reality. The study was designed to evaluate a multicomponent intervention involving 256 participants randomly assigned to one of 15 groups. Participants received either a minimal or an intense level of four intervention components: (1) nicotine replacement therapy, (2) precessation counseling, (3) cessation counseling, and (4) mHealth text messaging. The project team met via biweekly webinars as well as one to two in-person meetings per year throughout the study. The project …

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.

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.

The Odd Lindley Burr Xii Model: Bayesian Analysis, Classical Inference And Characterizations, Mustafa Ç. Korkmaz, Haitham M. Yousof, Mahdi Rasekhi, Gholamhossein G. Hamedani

Mathematical and Statistical Science Faculty Research and Publications

In this work, we study the odd Lindley Burr XII model initially introduced by Silva et al. [29]. This model has the advantage of being capable of modeling various shapes of aging and failure criteria. Some of its statistical structural properties including ordinary and incomplete moments, quantile and generating function and order statistics are derived. The odd Lindley Burr XII density can be expressed as a simple linear mixture of BurrXII densities. Useful characterizations are presented. The maximum likelihood method is used to estimate the model parameters. Simulation results to assess the performance of the maximum likelihood estimators are discussed. …