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Articles 1 - 21 of 21
Full-Text Articles in Physical Sciences and Mathematics
Disjoint And Simultaneously Hypercyclic Pseudo-Shifts, Nurhan Çolakoğlu, Özgür Martin, Rebecca Sanders
Disjoint And Simultaneously Hypercyclic Pseudo-Shifts, Nurhan Çolakoğlu, Özgür Martin, Rebecca Sanders
Mathematical and Statistical Science Faculty Research and Publications
We characterize disjoint and simultaneously hypercyclic tuples of unilateral pseudo-shift operators on ℓp(ℕ) . As a consequence, complementing the results of Bernal and Jung, we give a characterization for simultaneously hypercyclic tuples of unilateral weighted shifts. We also give characterizations for unilateral pseudo-shifts that satisfy the Disjoint and Simultaneous Hypercyclicity Criterions. Contrary to the disjoint hypercyclicity case, tuples of weighted shifts turn out to be simultaneously hypercyclic if and only if they satisfy the Simultaneous Hypercyclicity Criterion.
Functional Singular Spectrum Analysis, Hossein Haghbin, Seyed Morteza Najibi, Rahim Mahmoudvand, Jordan Trinka, Mehdi Maadooliat
Functional Singular Spectrum Analysis, Hossein Haghbin, Seyed Morteza Najibi, Rahim Mahmoudvand, Jordan Trinka, Mehdi Maadooliat
Mathematical and Statistical Science Faculty Research and Publications
In this paper, we develop a new extension of the singular spectrum analysis (SSA) called functional SSA to analyze functional time series. The new methodology is constructed by integrating ideas from functional data analysis and univariate SSA. Specifically, we introduce a trajectory operator in the functional world, which is equivalent to the trajectory matrix in the regular SSA. In the regular SSA, one needs to obtain the singular value decomposition (SVD) of the trajectory matrix to decompose a given time series. Since there is no procedure to extract the functional SVD (fSVD) of the trajectory operator, we introduce a computationally …
Characterizations And Reliability Measures Of The Generalized Log Burr Xii Distribution, Fiaz Ahmad Bhatti, Gholamhossein G. Hamedani, Azeem Ali, Sedigheh Mirzaei Salehabadi, Munir Ahmad
Characterizations And Reliability Measures Of The Generalized Log Burr Xii Distribution, Fiaz Ahmad Bhatti, Gholamhossein G. Hamedani, Azeem Ali, Sedigheh Mirzaei Salehabadi, Munir Ahmad
Mathematical and Statistical Science Faculty Research and Publications
In this paper, we derive the generalized log Burr XII (GLBXII) distribution [2] from the generalized Burr-Hatke differential equation. We characterize the GLBXII distribution via innovative techniques. We derive various reliability measures (series and parallel). We also authenticate the potentiality of the GLBXII model via economics applications. The applications of characterizations and reliability measures of the GLBXII distribution in different disciplines of science will be profitable for scientists.
Rapid Entry Into Masters In Computing Program For Non-Majors, Gary S. Krenz, Thomas Kaczmarek, John C. Moyer
Rapid Entry Into Masters In Computing Program For Non-Majors, Gary S. Krenz, Thomas Kaczmarek, John C. Moyer
Mathematical and Statistical Science Faculty Research and Publications
The COSMIC: Change Opportunity - Start Masters in Computing graduate curriculum initiative strives to provide a rapid entry pathway to a professional Master of Science (MS) degree for individuals who do not have an undergraduate degree in computing, but who wish to cross over to a career in the computing field. The goal of our curriculum is to minimize the time students spend preparing for graduate study and maximize experiences relevant for work after graduation. The COSMIC curriculum initiative is similar in concept to other post-baccalaureate conversion programs. However, customization of the COSMIC bridge course and curriculum pathway makes it …
A New Extended Alpha Power Transformed Family Of Distributions: Properties, Characterizations And An Application To A Data Set In The Insurance Sciences, Zubair Ahmad, Eisa Mahmoudi, Gholamhossein Hamedani
A New Extended Alpha Power Transformed Family Of Distributions: Properties, Characterizations And An Application To A Data Set In The Insurance Sciences, Zubair Ahmad, Eisa Mahmoudi, Gholamhossein Hamedani
Mathematical and Statistical Science Faculty Research and Publications
Heavy tailed distributions are useful for modeling actuarial and financial risk management problems. Actuaries often search for finding distributions that provide the best fit to heavy tailed data sets. In the present work, we introduce a new class of heavy tailed distributions of a special sub-model of the proposed family, called a new extended alpha power transformed Weibull distribution, useful for modeling heavy tailed data sets. Mathematical properties along with certain characterizations of the proposed distribution are presented. Maximum likelihood estimates of the model parameters are obtained. A simulation study is provided to evaluate the performance of the maximum likelihood …
Characterizations Of The Discrete Lindley And Discrete Poisson-Lindley Distributions, Gholamhossein G. Hamedani, Mahrokh Najaf
Characterizations Of The Discrete Lindley And Discrete Poisson-Lindley Distributions, Gholamhossein G. Hamedani, Mahrokh Najaf
Mathematical and Statistical Science Faculty Research and Publications
Certain characterizations of the discrete Lindley and discrete Poisson-Lindley distributions, originally introduced by Bakouch, Jazi and Nadarjah (2014) and Sankaran (1970), respectively, are presented. Al-Babtain, Gemeay and Afify (2020) revisited these distributions and provided estimation methods and actuarial measures as well as their applications in medicine. This short note is intended to complete, in some way, Al-Babtain, Gemeay and Afify (2020)’s work. It should be mentioned that the probability mass functions reported in the two papers mentioned above are not correct. In this note, it will be explained why they are not correct.
Exploring Prospective 1-8 Teachers' Number And Operation Sense In The Context Of Fractions, Marta T. Magiera, Leigh A. Van Den Kieboom
Exploring Prospective 1-8 Teachers' Number And Operation Sense In The Context Of Fractions, Marta T. Magiera, Leigh A. Van Den Kieboom
Mathematical and Statistical Science Faculty Research and Publications
This exploratory study examined prospective elementary teachers’ (PSTs’) number and operation sense (NOS) in the context of solving problems with fractions. Drawing on the existing literature, we identified seven skills that characterize fraction-related NOS. We analyzed 230 responses to 23 tasks completed by 10 PSTs for evidence of PSTs’ use of different fraction-related NOS skills. The analysis revealed that PSTs did not use all seven fraction-related NOS skills to the same extent. PSTs’ responses documented their frequent reasoning about the meaning of symbols and formal mathematical language in the context of fractions. To a lesser extent, PSTs’ responses documented their …
Sufficient Dimension Folding In Regression Via Distance Covariance For Matrix‐Valued Predictors, Wenhui Sheng, Qingcong Yuan
Sufficient Dimension Folding In Regression Via Distance Covariance For Matrix‐Valued Predictors, Wenhui Sheng, Qingcong Yuan
Mathematical and Statistical Science Faculty Research and Publications
In modern data, when predictors are matrix/array‐valued, building a reasonable model is much more difficult due to the complicate structure. However, dimension folding that reduces the predictor dimensions while keeps its structure is critical in helping to build a useful model. In this paper, we develop a new sufficient dimension folding method using distance covariance for regression in such a case. The method works efficiently without strict assumptions on the predictors. It is model‐free and nonparametric, but neither smoothing techniques nor selection of tuning parameters is needed. Moreover, it works for both univariate and multivariate response cases. In addition, we …
Cosmic: Us-Based Conversion Master's Degree In Computing, Gary S. Krenz, Thomas Kaczmarek
Cosmic: Us-Based Conversion Master's Degree In Computing, Gary S. Krenz, Thomas Kaczmarek
Mathematical and Statistical Science Faculty Research and Publications
COSMIC is an NSF S-STEM graduate curriculum initiative/conversion program that strives to provide an accelerated pathway to a Master of Science (MS) degree for individuals who do not have an undergraduate degree in computing, but who wish to cross over into the computing field. The structure of our conversion program, the context that motivated it, and insights from conversion students' instructors are presented. Program successes with students from under-represented populations and the limitations that are also experienced are discussed. Our conversion program is based on a highly focused summer bridge course, combined with a customized curriculum pathway that enables people …
The Marshall-Olkin Exponentiated Generalized G Family Of Distributions: Properties, Applications, And Characterizations, Haitham M. Yousof, Mahdi Rasekhi, Morad Alizadeh, Gholamhossein Hamedani
The Marshall-Olkin Exponentiated Generalized G Family Of Distributions: Properties, Applications, And Characterizations, Haitham M. Yousof, Mahdi Rasekhi, Morad Alizadeh, Gholamhossein Hamedani
Mathematical and Statistical Science Faculty Research and Publications
In this paper, we propose and study a new class of continuous distributions called the Marshall-Olkin exponentiated generalized G (MOEG-G) family which extends the Marshall-Olkin-G family introduced by Marshall and Olkin [A. W. Marshall, I. Olkin, Biometrika 84 (1997), 641-652]. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, order statistics and probability weighted moments are derived. Some characteristics of the new family are presented. Maximum likelihood estimation for the model parameters under uncensored and censored data is addressed in Section 5 as well as a simulation study to assess the performance of …
The Poisson Topp Leone Generator Of Distributions For Lifetime Data: Theory, Characterizations And Applications, Faton Merovci, Haitham M. Yousof, Gholamhossein Hamedani
The Poisson Topp Leone Generator Of Distributions For Lifetime Data: Theory, Characterizations And Applications, Faton Merovci, Haitham M. Yousof, Gholamhossein Hamedani
Mathematical and Statistical Science Faculty Research and Publications
We study a new family of distributions defined by the minimum of the Poisson random number of independent identically distributed random variables having a Topp Leone-G distribution (see Rezaei et al., (2016)). Some mathematical properties of the new family including ordinary and incomplete moments, quantile and generating functions, mean deviations, order statistics, reliability and entropies are derived. Maximum likelihood estimation of the model parameters is investigated. Some special models of the new family are discussed. An application is carried out on real data set applications sets to show the potentiality of the proposed family.
New Modified Singh-Maddala Distribution: Development, Properties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein G. Hamedani, Mustafa Ç. Korkmaz, Munir Ahmad
New Modified Singh-Maddala 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 five-parameter extended Burr XII model called new modified Singh-Maddala (NMSM) is developed from cumulative hazard function of the modified log extended integrated beta hazard (MLEIBH) model. The NMSM density function is left-skewed, right-skewed and symmetrical. The Lambert W function is used to study descriptive measures based on quantile, moments, and moments of order statistics, incomplete moments, inequality measures and residual life function. Different reliability and uncertainty measures are also theoretically established. The NMSM distribution is characterized via different techniques and its parameters are estimated using maximum likelihood method. The simulation studies are performed on the …
Characterizations Of Marshall-Olkin Discrete Reduced Modified Weibull Distribution, Gholamhossein G. Hamedani
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.
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
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. …
The Zero Truncated Poisson Burr X Family Of Distributions With Properties, Characterizations, Applications, And Validation Test, T. H.M. Aboulemagd, Mohammed S. Hamed, Gholamhossein Hamedani, M. M. Ali, Hafida Goual, Mustafa Ç. Korkmaz, Haitham M. Yousof
The Zero Truncated Poisson Burr X Family Of Distributions With Properties, Characterizations, Applications, And Validation Test, T. H.M. Aboulemagd, Mohammed S. Hamed, Gholamhossein Hamedani, M. M. Ali, Hafida Goual, Mustafa Ç. Korkmaz, Haitham M. Yousof
Mathematical and Statistical Science Faculty Research and Publications
The goal of this work is to introduce a new family of continuous distributions with a strong physical application. Some statistical properties are derived, and certain useful characterizations of the proposed family distributions are presented. Five applications are provided to illustrate the importance of the new family. A modified goodness-of-fit test for the new family in complete data case are investigated via two examples. We propose, as a first step, the construction of Nikulin-Rao-Robson statistic based on chi-squared fit tests for the new family in the case of complete data. The new test is based on the Nikulin-Rao-Robson statistic separately …
On The Exponentiated Weibull Rayleigh Distribution, Mohammed Elgarhy, Ibrahim Elbatal, Gholamhossein G. Hamedani, Amal Hassan
On The Exponentiated Weibull Rayleigh Distribution, Mohammed Elgarhy, Ibrahim Elbatal, Gholamhossein G. Hamedani, Amal Hassan
Mathematical and Statistical Science Faculty Research and Publications
A new four-parameter probability model, referred to the exponentiated Weibull Rayleigh (EWR) distribution, is introduced. Essential statistical properties of the distribution are considered. The maximum likelihood estimators of population parameters are given in case of complete sample. Simulation study is carried out to estimate the model parameters of EWR distribution. Additionally, parameter estimators are given in case of Type II censored samples. We come up with two applications to confirm the usefulness of the proposed distribution.
The Extended Alpha Power Transformed Family Of Distributions: Properties And Applications, Zubair Ahmad, Muhammad Ilyas, Gholamhossein G. Hamedani
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 …
Mathematical Modeling Experiences: Narratives From A Preservice Teacher And An Instructor, Sarah Brand, Hyunyi Jung
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.
Group Presentations As A Site For Collective Modeling Activity, Corey Brady, Hyunyi Jung
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, …
Mathematical Modeling And Classroom Discourse: A Case For Modeling-Specific Discussion Strategies, Ashley Dorlack, Hyunyi Jung, Sarah Brand, Samuel Franklin Gailliot
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.
The Odd Lindley Burr Xii Model: Bayesian Analysis, Classical Inference And Characterizations, Mustafa Ç. Korkmaz, Haitham M. Yousof, Mahdi Rasekhi, Gholamhossein G. Hamedani
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. …