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Articles 1 - 30 of 33
Full-Text Articles in Mathematics
Quantification Of The Statistical Effects Of Spatiotemporal Processing Of Nontask Fmri Data, M. Muge Karaman, Andrew S. Nencka, Iain P. Bruce, Daniel B. Rowe
Quantification Of The Statistical Effects Of Spatiotemporal Processing Of Nontask Fmri Data, M. Muge Karaman, Andrew S. Nencka, Iain P. Bruce, Daniel B. Rowe
Mathematics, Statistics and Computer Science Faculty Research and Publications
Nontask functional magnetic resonance imaging (fMRI) has become one of the most popular noninvasive areas of brain mapping research for neuroscientists. In nontask fMRI, various sources of “noise” corrupt the measured blood oxygenation level-dependent signal. Many studies have aimed to attenuate the noise in reconstructed voxel measurements through spatial and temporal processing operations. While these solutions make the data more “appealing,” many commonly used processing operations induce artificial correlations in the acquired data. As such, it becomes increasingly more difficult to derive the true underlying covariance structure once the data have been processed. As the goal of nontask fMRI studies …
Correction To “Master Regulators, Regulatory Networks, And Pathways Of Glioblastoma Subtypes”, Serdar Bozdag, Aiguo Li, Mehmet Baysan, Howard A. Fine
Correction To “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
No abstract provided.
Remarks On Characterizations Of Malinowska And Szynal, Gholamhossein Hamedani, Z. Javanshiri, Mehdi Maadooliat, A. Yazdani
Remarks On Characterizations Of Malinowska And Szynal, Gholamhossein Hamedani, Z. Javanshiri, Mehdi Maadooliat, A. Yazdani
Mathematics, Statistics and Computer Science Faculty Research and Publications
The problem of characterizing a distribution is an important problem which has recently attracted the attention of many researchers. Thus, various characterizations have been established in many different directions. An investigator will be vitally interested to know if their model fits the requirements of a particular distribution. To this end, one will depend on the characterizations of this distribution which provide conditions under which the underlying distribution is indeed that particular distribution. In this work, several characterizations of Malinowska and Szynal (2008) for certain general classes of distributions are revisited and simpler proofs of them are presented. These characterizations are …
The Antisymmetry Betweenness Axiom And Hausdorff Continua, Paul Bankston
The Antisymmetry Betweenness Axiom And Hausdorff Continua, Paul Bankston
Mathematics, Statistics and Computer Science Faculty Research and Publications
An interpretation of betweenness on a set satisfies the antisymmetry axiom at a point a if it is impossible for each of two distinct points to lie between the other and a. In this paper we study the role of antisymmetry as it applies to the K-interpretation of betweenness in a Hausdorff continuum X, where a point c lies between points a and b exactly when every subcontinuum of X containing both a and b contains c as well.
Relatively Congruence-Free Regular Semigroups, Peter Jones
Relatively Congruence-Free Regular Semigroups, Peter Jones
Mathematics, Statistics and Computer Science Faculty Research and Publications
Yu, Wang, Wu and Ye call a semigroup S τ -congruence-free, where τ is an equivalence relation on S, if any congruence ρ on S is either disjoint from τ or contains τ . A congruence-free semigroup is then just an ω-congruence-free semigroup, where ω is the universal relation. They determined the completely regular semigroups that are τ -congruence-free with respect to each of the Green’s relations. The goal of this paper is to extend their results to all regular semigroups. Such a semigroup is J –congruence-free if and only if it is either a semilattice or has …
Some Remarks On Recent Characterizations Of Continuous Distributions, Gholamhossein Hamedani
Some Remarks On Recent Characterizations Of Continuous Distributions, Gholamhossein Hamedani
Mathematics, Statistics and Computer Science Faculty Research and Publications
We would closely look at two recent published papers dealing with characterizations of certain univariate continuous distributions. We shall explain that the main results reported lack important assumptions. These results nevertheless are based on the conditional expectations of monotone functions of the generalized order statistics. We will also mention that similar results have recently been reported without the assumption of monotonicity of the functions of the generalized order statistics.
Exploring The Relationship Between K-8 Prospective Teachers’ Algebraic Thinking Proficiency And The Questions They Pose During Diagnostic Algebraic Thinking Interviews, Leigh A. Van Den Kieboom, Marta T. Magiera, John C. Moyer
Exploring The Relationship Between K-8 Prospective Teachers’ Algebraic Thinking Proficiency And The Questions They Pose During Diagnostic Algebraic Thinking Interviews, Leigh A. Van Den Kieboom, Marta T. Magiera, John C. Moyer
Mathematics, Statistics and Computer Science Faculty Research and Publications
In this study, we explored the relationship between prospective teachers’ algebraic thinking and the questions they posed during one-on-one diagnostic interviews that focused on investigating the algebraic thinking of middle school students. To do so, we evaluated prospective teachers’ algebraic thinking proficiency across 125 algebra-based tasks and we analyzed the characteristics of questions they posed during the interviews. We found that prospective teachers with lower algebraic thinking proficiency did not ask any probing questions. Instead, they either posed questions that simply accepted and affirmed student responses or posed questions that guided the students toward an answer without probing student thinking. …
Generalized Exponentiated Moment Exponential Distribution, Zafar Iqbal, Syed Anwer Hasnain, Muhammad Salman, Munir Ahmad, Gholamhossein Hamedani
Generalized Exponentiated Moment Exponential Distribution, Zafar Iqbal, Syed Anwer Hasnain, Muhammad Salman, Munir Ahmad, Gholamhossein Hamedani
Mathematics, Statistics and Computer Science Faculty Research and Publications
Moment distributions have a vital role in mathematics and statistics, in particular in probability theory, in the perspective research related to ecology, reliability, biomedical field, econometrics, survey sampling and in life-testing. Hasnain (2013) developed an exponentiated moment exponential (EME) distribution and discussed some of its important properties. In the present work, we propose a generalization of EME distribution which we call it generalized EME (GEME) distribution and develop various properties of the distribution. We also present characterizations of the distribution in terms of conditional expectation as well as based on hazard function of the GEME random variable.
Characterizations Of A Class Of Distributions By Dual Generalized Order Statistics And Truncated Moments, Filippo Domma, Gholamhossein Hamedani
Characterizations Of A Class Of Distributions By Dual Generalized Order Statistics And Truncated Moments, Filippo Domma, Gholamhossein Hamedani
Mathematics, Statistics and Computer Science Faculty Research and Publications
The problem of characterizing a distribution is an important problem which has recently attracted the attention of many researchers. Thus, various characterizations have been established in many different directions. The present work deals with the characterizations of a general class of distributions. These characterizations are based on: (i) a simple relationship between two truncated moments, (ii) truncated moment of certain functions of the nth order statistic, (iii) single truncated moment of certain functions of the random variable and (iv) moments of dual generalized order statistics.We like to mention that the characterization (i) which is expressed in terms of the ratio …
Pharyngeal And Cervical Cancer Incidences Significantly Correlate With Personal Uv Doses Among Whites In The United States, Dianne E. Godar, Rong Tang, Stephen Merrill
Pharyngeal And Cervical Cancer Incidences Significantly Correlate With Personal Uv Doses Among Whites In The United States, Dianne E. Godar, Rong Tang, Stephen Merrill
Mathematics, Statistics and Computer Science Faculty Research and Publications
Because we found UV-exposed oral tissue cells have reduced DNA repair and apoptotic cell death compared with skin tissue cells, we asked if a correlation existed between personal UV dose and the incidences of oral and pharyngeal cancer in the United States. We analyzed the International Agency for Research on Cancer's incidence data for oral and pharyngeal cancers by race (white and black) and sex using each state's average annual personal UV dose. We refer to our data as ‘white’ rather than ‘Caucasian,’ which is a specific subgroup of whites, and ‘black’ rather than African-American because blacks from other countries …
Existence Of Disjoint Weakly Mixing Operators That Fail To Satisfy The Disjoint Hypercyclicity Criterion, Rebecca Sanders, Stanislav Shkarin
Existence Of Disjoint Weakly Mixing Operators That Fail To Satisfy The Disjoint Hypercyclicity Criterion, Rebecca Sanders, Stanislav Shkarin
Mathematics, Statistics and Computer Science Faculty Research and Publications
No abstract provided.
Towards A Lightweight Approach For Modding Serious Educational Games: Assisting Novice Designers, Jacob Dahleen, Alex Hunsberger, Ryan Weber, Dennis Brylow, C. Shaun Longstreet, Kendra M. L. Cooper
Towards A Lightweight Approach For Modding Serious Educational Games: Assisting Novice Designers, Jacob Dahleen, Alex Hunsberger, Ryan Weber, Dennis Brylow, C. Shaun Longstreet, Kendra M. L. Cooper
Mathematics, Statistics and Computer Science Faculty Research and Publications
Serious educational games (SEGs) are a growing segment of the education community’s pedagogical toolbox. Effectively creating such games remains challenging, as teachers and industry trainers are content experts; typically they are not game designers with the theoretical knowledge and practical experience needed to create a quality SEG. Here, a lightweight approach to interactively explore and modify existing SEGs is introduced, a toll that can be broadly adopted by educators for pedagogically sound SEGs. Novice game designers can rapidly explore the educational and traditional elements of a game, with a stress on tracking the SEG learning objectives, as well as allowing …
Better Physical Activity Classification Using Smartphone Acceleration Sensor, Muhammad Arif, Mohsin Bilal, Ahmed Kattan, Sheikh Iqbal Ahamed
Better Physical Activity Classification Using Smartphone Acceleration Sensor, Muhammad Arif, Mohsin Bilal, Ahmed Kattan, Sheikh Iqbal Ahamed
Mathematics, Statistics and Computer Science Faculty Research and Publications
Obesity is becoming one of the serious problems for the health of worldwide population. Social interactions on mobile phones and computers via internet through social e-networks are one of the major causes of lack of physical activities. For the health specialist, it is important to track the record of physical activities of the obese or overweight patients to supervise weight loss control. In this study, acceleration sensor present in the smartphone is used to monitor the physical activity of the user. Physical activities including Walking, Jogging, Sitting, Standing, Walking upstairs and Walking downstairs are classified. Time domain features are extracted …
The Inferred Cardiogenic Gene Regulatory Network In The Mammalian Heart, Jason Bazil, Karl D. Stamm, Xing Li, Raghuram Thiagarajan, Timonthy J. Nelson, Aoy Tomita-Mitchell, Daniel A. Beard
The Inferred Cardiogenic Gene Regulatory Network In The Mammalian Heart, Jason Bazil, Karl D. Stamm, Xing Li, Raghuram Thiagarajan, Timonthy J. Nelson, Aoy Tomita-Mitchell, Daniel A. Beard
Mathematics, Statistics and Computer Science Faculty Research and Publications
Cardiac development is a complex, multiscale process encompassing cell fate adoption, differentiation and morphogenesis. To elucidate pathways underlying this process, a recently developed algorithm to reverse engineer gene regulatory networks was applied to time-course microarray data obtained from the developing mouse heart. Approximately 200 genes of interest were input into the algorithm to generate putative network topologies that are capable of explaining the experimental data via model simulation. To cull specious network interactions, thousands of putative networks are merged and filtered to generate scale-free, hierarchical networks that are statistically significant and biologically relevant. The networks are validated with known gene …
Counting Independent Sets Of A Fixed Size In Graphs With Given Minimum Degree, John Engbers, David Galvin
Counting Independent Sets Of A Fixed Size In Graphs With Given Minimum Degree, John Engbers, David Galvin
Mathematics, Statistics and Computer Science Faculty Research and Publications
Galvin showed that for all fixed δ and sufficiently large n, the n-vertex graph with minimum degree δ that admits the most independent sets is the complete bipartite graph . He conjectured that except perhaps for some small values of t, the same graph yields the maximum count of independent sets of size t for each possible t. Evidence for this conjecture was recently provided by Alexander, Cutler, and Mink, who showed that for all triples with , no n-vertex bipartite graph with minimum degree δ admits more independent sets of size t than . …
Regularized Multivariate Regression Models With Skew-T Error Distributions, Lianfu Chen, Mohsen Pourahmadi, Mehdi Maadooliat
Regularized Multivariate Regression Models With Skew-T Error Distributions, Lianfu Chen, Mohsen Pourahmadi, Mehdi Maadooliat
Mathematics, Statistics and Computer Science Faculty Research and Publications
We consider regularization of the parameters in multivariate linear regression models with the errors having a multivariate skew-t distribution. An iterative penalized likelihood procedure is proposed for constructing sparse estimators of both the regression coefficient and inverse scale matrices simultaneously. The sparsity is introduced through penalizing the negative log-likelihood by adding L1-penalties on the entries of the two matrices. Taking advantage of the hierarchical representation of skew-t distributions, and using the expectation conditional maximization (ECM) algorithm, we reduce the problem to penalized normal likelihood and develop a procedure to minimize the ensuing objective function. Using a …
Beta Burr Xii Or Five Parameter Beta Lomax Distribution: Remarks And Characterizations, Z. Javanshiri, Mehdi Maadooliat
Beta Burr Xii Or Five Parameter Beta Lomax Distribution: Remarks And Characterizations, Z. Javanshiri, Mehdi Maadooliat
Mathematics, Statistics and Computer Science Faculty Research and Publications
The distributions taken up in two recently published papers are compared and certain characterizations of them are presented. These characterizations are based on: (i) a simple relationship between two truncated moments; (ii) truncated moments of certain functions of the nth order statistic; (iii) truncated moments of certain functions of the random variable.
Highly Sensitive Noninvasive Cardiac Transplant Rejection Monitoring Using Targeted Quantification Of Donor-Specific Cell-Free Deoxyribonucleic Acid, Mats Hidestrand, Aoy Tomita-Mitchell, Pip M. Hidestrand, Arnold Oliphant, Mary Goetsch, Karl D. Stamm, Huan-Ling Liang, Chesney Castleberry, D. Woodrow Benson, Gail Stendahl, Pippa Simpson, Stuart Berger, James S. Tweddell, Steven Zangwill, Michael E. Mitchell
Highly Sensitive Noninvasive Cardiac Transplant Rejection Monitoring Using Targeted Quantification Of Donor-Specific Cell-Free Deoxyribonucleic Acid, Mats Hidestrand, Aoy Tomita-Mitchell, Pip M. Hidestrand, Arnold Oliphant, Mary Goetsch, Karl D. Stamm, Huan-Ling Liang, Chesney Castleberry, D. Woodrow Benson, Gail Stendahl, Pippa Simpson, Stuart Berger, James S. Tweddell, Steven Zangwill, Michael E. Mitchell
Mathematics, Statistics and Computer Science Faculty Research and Publications
No abstract provided.
Micro-Environment Causes Reversible Changes In Dna Methylation And Mrna Expression Profiles In Patient-Derived Glioma Stem Cells, Mehmet Baysan, Kevin Woolard, Serdar Bozdag, Gregory Riddick, Svetlana Kotliarova, Margaret C. Cam, Galina I. Belova, Susie Ahn, Wei Zhang, Hua Song, Jennifer Walling, Holly Stevenson, Paul Meltzer, Howard A. Fine
Micro-Environment Causes Reversible Changes In Dna Methylation And Mrna Expression Profiles In Patient-Derived Glioma Stem Cells, Mehmet Baysan, Kevin Woolard, Serdar Bozdag, Gregory Riddick, Svetlana Kotliarova, Margaret C. Cam, Galina I. Belova, Susie Ahn, Wei Zhang, Hua Song, Jennifer Walling, Holly Stevenson, Paul Meltzer, Howard A. Fine
Mathematics, Statistics and Computer Science Faculty Research and Publications
In vitro and in vivo models are widely used in cancer research. Characterizing the similarities and differences between a patient's tumor and corresponding in vitro and in vivo models is important for understanding the potential clinical relevance of experimental data generated with these models. Towards this aim, we analyzed the genomic aberrations, DNA methylation and transcriptome profiles of five parental tumors and their matched in vitro isolated glioma stem cell (GSC) lines and xenografts generated from these same GSCs using high-resolution platforms. We observed that the methylation and transcriptome profiles of in vitro GSCs were significantly different from their corresponding …
Mcdonald Log-Logistic Distribution With An Application To Breast Cancer Data, M. H. Tahir, Muhammad Mansoor, Muhammad Zubair, Gholamhossein Hamedani
Mcdonald Log-Logistic Distribution With An Application To Breast Cancer Data, M. H. Tahir, Muhammad Mansoor, Muhammad Zubair, Gholamhossein Hamedani
Mathematics, Statistics and Computer Science Faculty Research and Publications
We introduce a five-parameter continuous model, called the McDonald log-logistic distribution, to extend the two-parameter log-logistic distribution. Some structural properties of this new distribution such as reliability measures and entropies are obtained. The model parameters are estimated by the method of maximum likelihood using L-BFGS-B algorithm. A useful characterization of the distribution is proposed which does not require explicit closed form of the cumulative distribution function and also connects the probability density function with a solution of a first order differential equation. An application of the new model to real data set shows that it can give consistently better fit …
Quantifying The Statistical Impact Of Grappa In Fcmri Data With A Real-Valued Isomorphism, Iain P. Bruce, Daniel B. Rowe
Quantifying The Statistical Impact Of Grappa In Fcmri Data With A Real-Valued Isomorphism, Iain P. Bruce, Daniel B. Rowe
Mathematics, Statistics and Computer Science Faculty Research and Publications
The interpolation of missing spatial frequencies through the generalized auto-calibrating partially parallel acquisitions (GRAPPA) parallel magnetic resonance imaging (MRI) model implies a correlation is induced between the acquired and reconstructed frequency measurements. As the parallel image reconstruction algorithms in many medical MRI scanners are based on the GRAPPA model, this study aims to quantify the statistical implications that the GRAPPA model has in functional connectivity studies. The linear mathematical framework derived in the work of Rowe , 2007, is adapted to represent the complex-valued GRAPPA image reconstruction operation in terms of a real-valued isomorphism, and a statistical analysis is performed …
When Semi-Monotone Implies Monotone, Paul Bankston
When Semi-Monotone Implies Monotone, Paul Bankston
Mathematics, Statistics and Computer Science Faculty Research and Publications
The basic theme of this talk is the extrinsic description of objects by means of morphisms. One way to do this is to say that all monomorphisms from the object are “special” in some way; the dual of this is to single out epimorphisms to the object.
Remarks On A Paper Of Lee And Lim, Gholamhossein Hamedani, Michael Slattery
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 …
Characterizations Of New Modified Weibull Distribution, Gholamhossein Hamedani
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.
A Statistical Fmri Model For Differential T2* Contrast Incorporating T1 And T2* Of Gray Matter, M. Muge Karaman, Iain P. Bruce, Daniel B. Rowe
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 …
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
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 …
Trivial Meet And Join Within The Lattice Of Monotone Triangles, John Engbers, Adam Hammett
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 τmin denote the unique minimal element in this lattice, and τmax the unique maximum. The number of r-tuples of monotone triangles (τ1...,τr) with minimul infimum τmin (maximul supremum τmax, resp.) is shown to asymptotically approach r|�n|r-1 as n→ ∞. Thus, with high probability this even implies that one of the τi is τmin (τmax, resp.). Higher-order error terms are also discussed.
Varieties Of P-Restriction Semigroups, Peter R. Jones
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 …
Master Regulators, Regulatory Networks, And Pathways Of Glioblastoma Subtypes, Serdar Bozdag, Aiguo Li, Mehmet Baysan, Howard A. Fine
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 …
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
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.