Mathematics Commons^™

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 …

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) …

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 …

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 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 …

A Bayesian Nonparametric Multiple Testing Procedure For Comparing Several Treatments Against A Control, Luis Gutiérrez, Andrés Barrientos, Jorge González, Daniel Taylor-Rodríguez

Mathematics and Statistics Faculty Publications and Presentations

We propose a Bayesian nonparametric strategy to test for differences between a control group and several treatment regimes. Most of the existing tests for this type of comparison are based on the differences between location parameters. In contrast, our approach identifies differences across the entire distribution, avoids strong modeling assumptions over the distributions for each treatment, and accounts for multiple testing through the prior distribution on the space of hypotheses. The proposal is compared to other commonly used hypothesis testing procedures under simulated scenarios. Two real applications are also analyzed with the proposed methodology.

Stability Conditions For Coupled Oscillators In Linear Arrays, Pablo Enrique Baldivieso Blanco, J.J.P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

In this paper, we give necessary conditions for stability of flocks in R. We focus on linear arrays with decentralized agents, where each agent interacts with only a few its neighbors. We obtain explicit expressions for necessary conditions for asymptotic stability in the case that the systems consists of a periodic arrangement of two or three different types of agents, i.e. configurations as follows: ...2-1-2-1 or ...3-2-1-3-2-1. Previous literature indicated that the (necessary) condition for stability in the case of a single agent (...1-1-1) held that the first moment of certain coefficients governing the interactions between agents has to be …

Counting And Coloring Sudoku Graphs, Kyle Oddson

Mathematics and Statistics Dissertations, Theses, and Final Project Papers

A sudoku puzzle is most commonly a 9 × 9 grid of 3 × 3 boxes wherein the puzzle player writes the numbers 1 - 9 with no repetition in any row, column, or box. We generalize the notion of the n² × n² sudoku grid for all n ∈ ℤ^≥2 and codify the empty sudoku board as a graph. In the main section of this paper we prove that sudoku boards and sudoku graphs exist for all such n; we prove the equivalence of [3]'s construction using unions and products of graphs to the definition of …

Domain Decomposition Methods For The Solution Of Multiple Scattering Problems, Michael Pedneault

Dissertations

This presents a Schur complement Domain Decomposition (DD) algorithm for the solution of frequency domain multiple scattering problems. Just as in the classical DD methods,(1) the ensemble of scatterers is enclosed in a domain bounded by an artificial boundary, (2) this domain is subdivided into a collection of nonoverlapping subdomains so that the boundaries of the subdomains do not intersect any of the scatterers, and (3) the solutions of the subproblems are connected via Robin boundary conditions matching on the common interfaces between subdomains. Subdomain Robin-to-Robin maps are used to recast the DD problem as a sparse linear system whose …

Fwer Controlling Procedures In Simultaneous And Selective Inference, Li Yu

Dissertations

With increasing complexity of research objectives in clinical trials, a variety of relatively complex and less intuitive multiple testing procedures (MTPs) have been developed and applied in clinical data analysis. In order to make testing strategies more explicit and intuitive to communicate with non-statisticians, several flexible and powerful graphical approaches have recently been introduced in the literature for developing and visualizing newer MTPs. Nevertheless, some theoretical as well as methodological issues still remain to be fully addressed. This dissertation addresses several important issues arising in graphical approaches and related selective inference problems. It consists of three parts.

In the first …

Optimasi Perencanaan Produksi Bahan Bakar Minyak Dengan Fungsi Kendala Fuzzy Menggunakan Metode Goal Programming, Wiwiet Widyaningsih, Sri Andayani

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

Dalam perencanaan produksi PT. Pertamina (Persero) TBBM Boyolali, perusahaan tersebut hanya mendistribusikan BBM sesuai dengan permintaan SPBU tanpa melakukan perhitungan matematis apakah pendapatan yang diperoleh sudah optimal dengan semua faktor dan kendala yang ada, seperti harga setiap jenis BBM, jam kerja mesin pengisian BBM di New Gantry System (NGS), moda transport mobil tangki, dan tingkat keselamatan mobil tangki. Untuk itu, penelitian ini bertujuan untuk melakukan optimasi perencanaan produksi BBM menggunakan metode goal programming agar perusahaan dapat memperoleh pendapatan yang maksimal dengan memperhatikan faktor-faktor dan kendala yang ada. Metode goal programming merupakan perluasan dari linear programming yang dapat menyelesaikan optimasi dengan …

Model Matematis Predator-Prey Tanaman Padi, Hama Penggerek Batang, Tikus, Dan Wereng Batang Coklat Di Karawang, Tesa Nur Padilah, Betha Nurina Sari, Hannie Hannie

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

Karawang merupakan salah satu pusat penanaman padi di Pulau Jawa. Keberhasilan panen dapat terganggu oleh adanya organisme pengganggu tumbuhan (OPT) sehingga dapat mengancam target swasembada beras. Hubungan antara tanaman padi dengan OPT dapat dibentuk menjadi suatu model matematis yaitu model predator-prey. Untuk itu, penelitian ini bertujuan untuk menganalisis model matematis predator-prey tanaman padi dan OPT. Predator (pemangsa) adalah makhluk hidup yang memakan mangsa (prey). Model predator-prey antara tanaman padi dengan OPT yang dibahas adalah model tiga predator yaitu hama penggerek batang, tikus, dan wereng batang coklat dengan prey yaitu padi. Pertumbuhan padi mengikuti …

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 …

Find, Process, And Share: An Optimal Control In The Vidale-Wolfe Marketing Model, Michael C. Barg

CODEE Journal

The Vidale-Wolfe marketing model is a first-order, linear, non-homogeneous ordinary differential equation (ODE) where the forcing term is proportional to advertising expenditure. With an initial response in sales as the initial condition, the solution of the initial value problem is straightforward for a first undergraduate ODE course. The model serves as an excellent example of many relevant topics for those students whose interests lie in economics, finance, or marketing. Its inclusion in the curriculum is particularly rewarding at an institution without a physics program. The model is not new, but it was novel to us when a group of students …

Lozenge Tilings Of A Halved Hexagon With An Array Of Triangles Removed From The Boundary, Part Ii, Tri Lai

Department of Mathematics: Faculty Publications

Proctor's work on staircase plane partitions yields an exact enumeration of lozenge tilings of a halved hexagon on the triangular lattice. Rohatgi later ex- tended this tiling enumeration to a halved hexagon with a triangle cut o from the boundary. In his previous paper, the author proved a common generalization of Proctor's and Rohatgi's results by enumerating lozenge tilings of a halved hexagon in the case an array of an arbitrary number of triangles has been removed from a non-staircase side. In this paper we consider the other case when the array of tri- angles has been removed from the …

Numerical Simulation Of Dropped Cylindrical Objects Into Water In Two Dimensions (2d), Yi Zhen

LSU New Orleans Theses and Dissertations

The dropped objects are identified as one of the top ten causes of fatalities and serious injuries in the oil and gas industry. It is of importance to understand dynamics of dropped objects under water in order to accurately predict the motion of dropped objects and protect the underwater structures and facilities from being damaged. In this thesis, we study nondimensionalization of dynamic equations of dropped cylindrical objects. Nondimensionalization helps to reduce the number of free parameters, identify the relative size of effects of parameters, and gain a deeper insight of the essential nature of dynamics of dropped cylindrical objects …

Power In Pairs: Assessing The Statistical Value Of Paired Samples In Tests For Differential Expression, John R. Stevens, Jennifer S. Herrick, Roger K. Wolff, Martha L. Slattery

Mathematics and Statistics Faculty Publications

Background: When genomics researchers design a high-throughput study to test for differential expression, some biological systems and research questions provide opportunities to use paired samples from subjects, and researchers can plan for a certain proportion of subjects to have paired samples. We consider the effect of this paired samples proportion on the statistical power of the study, using characteristics of both count (RNA-Seq) and continuous (microarray) expression data from a colorectal cancer study.

Results: We demonstrate that a higher proportion of subjects with paired samples yields higher statistical power, for various total numbers of samples, and for various strengths of …

Limit Properties Of Order Statistics, А. Madraximov, S. Kukieva

Scientific journal of the Fergana State University

The paper studies the question of estimating the concentration function for the sums of minima of positive random variables.

Substantiation The Parameters Of The Cotton Cleaners’ Polyhedral Vibrating Fire-Bars, A. Djuraev, R.Kh. Maksudov, Sh. Shukhratov

Scientific journal of the Fergana State University

The article describes the principle of operation of the recommended multifaceted grate on elastic supports, as well as the results of the analysis of the grate oscillations, and the parameters are justified. The results of comparative production tests.

Mathematical Models For The Numerical Solution Of Boundary Value Problems Nonstationary Three-Phase Filtering, А. Abdukodirov, G. Аkramova

Scientific journal of the Fergana State University

The construction of an explicit / implicit scheme for the numerical solution of regional problems of non-stationary three-phase filtration is considered in the article.