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Full-Text Articles in Physical Sciences and Mathematics

Measuring Irregularity Via Approximate Entropy: How Does Perceived Human Instability Affect One's Own Stability?, Madi Braunersrither Dec 2021

Measuring Irregularity Via Approximate Entropy: How Does Perceived Human Instability Affect One's Own Stability?, Madi Braunersrither

Fall Student Research Symposium 2021

In a study performed at Utah State University, participants were prompted to evaluate the stability of pictured human postures while standing on a force plate. The force plate was used to collect the center of pressure of the subjects by recording measurements in the vertical and horizontal directions. The way these factors fluctuate over time and the irregularity in this fluctuation, specifically, can give insight into the subject’s postural stability. Rather than working with summary statistics such as means and variances of fitting parameters of a distribution as commonly done in statistics, we want to measure irregularity through analyzing the …

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Creating Transparent And Accessible Methods For Approximating The Composite Strength Of Concrete Sandwich Wall Panels, Ruth Taylor Dec 2021

Creating Transparent And Accessible Methods For Approximating The Composite Strength Of Concrete Sandwich Wall Panels, Ruth Taylor

Fall Student Research Symposium 2021

Background: The method of designing partially composite sandwich wall panels (SWPs) relies strongly on the use of percent of composite action. Calculating these values proves to be a complex and virtually inaccessible process for practicing engineers, resulting in the reliance on proprietary software or connector-system manufacturers for the necessary values. We simulated percent composite action data, including several relevant variables, to examine the relationship and determine if simple and accessible methods of calculation could be created. Methods: Code from collaborating engineers used to calculate percent composite action with the Iterative Sandwich Beam Theory (ISBT) method was translated into R, a …

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Nutrient Intake And Dietary Inflammatory Potential In Current And Recovered Anorexia Nervosa, Olivia Patsalos, Bethan Dalton, Christia Kyprianou, Joseph Firth, Nitin Shivappa Mbbs, Mph, Ph.D., James Hébert Scd, Ulrike Schmidt, Hubertus Himmerich Dec 2021

Nutrient Intake And Dietary Inflammatory Potential In Current And Recovered Anorexia Nervosa, Olivia Patsalos, Bethan Dalton, Christia Kyprianou, Joseph Firth, Nitin Shivappa Mbbs, Mph, Ph.D., James Hébert Scd, Ulrike Schmidt, Hubertus Himmerich

Faculty Publications

Anorexia nervosa (AN) is characterised by disrupted and restrictive eating patterns. Recent investigations and meta-analyses have found altered concentrations of inflammatory markers in people with current AN. We aimed to assess nutrient intake in participants with current or recovered AN, as compared to healthy individuals, and explore group differences in dietary inflammatory potential as a possible explanation for the observed alterations in inflammatory markers. We recruited participants with current AN (n = 51), those recovered from AN (n = 23), and healthy controls (n = 49). We used the Food Frequency Questionnaire (FFQ), to calculate a Dietary …

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Teacher Education Programs Of Top Pisa Scoring Countries, Stephanie Kafer Dec 2021

Teacher Education Programs Of Top Pisa Scoring Countries, Stephanie Kafer

Honors Projects

This research paper aims to investigate the teacher education programs of four different countries that have consistently scored high on the international Programme for International Student Assessment (PISA) test. This project intends to answer two questions: What locations consistently perform high on the Programme for International Student Assessment (PISA) test? What do the teacher training programs look like for these locations and are there commonalities between programs of different locations? The first question is answered using statistics of PISA scores from the past twenty years and from those statistics, the top four countries that this paper focuses on are Finland, …

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Non-Parametric Tests For Testing Of Scale Parameters, Manish Goyal, Narinder Kumar Dec 2021

Non-Parametric Tests For Testing Of Scale Parameters, Manish Goyal, Narinder Kumar

Journal of Modern Applied Statistical Methods

One of the fundamental problems in testing of equality of populations is of testing the equality of scale parameters. The subsequent usages for scale are dispersion, spread and variability. In this paper, we proposed non-parametric tests based on U-Statistics for the testing of equality of scale parameters. The null distribution of proposed tests is developed and its Pitman efficiency is worked out to compare proposed tests with respect to some existing tests. Simulation study is carried out to compute the asymptotic power of proposed tests. An illustrative example is also provided.

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(R1239) A New Type Ii Half Logistic-G Family Of Distributions With Properties, Regression Models, System Reliability And Applications, Emrah Altun, Morad Alizadeh, Haitham M. Yousof, Mahdi Rasekhi, G. G. Hamedani Dec 2021

(R1239) A New Type Ii Half Logistic-G Family Of Distributions With Properties, Regression Models, System Reliability And Applications, Emrah Altun, Morad Alizadeh, Haitham M. Yousof, Mahdi Rasekhi, G. G. Hamedani

Applications and Applied Mathematics: An International Journal (AAM)

This study proposes a new family of distributions based on the half logistic distribution. With the new family, the baseline distributions gain flexibility through additional shape parameters. The important statistical properties of the proposed family are derived. A new generalization of the Weibull distribution is used to introduce a location-scale regression model for the censored response variable. The utility of the introduced models is demonstrated in survival analysis and estimation of the system reliability. Three data sets are analyzed. According to the empirical results, it is observed that the proposed family gives better results than other existing models.

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Oscillation Of Nonlinear Third-Order Difference Equations With Mixed Neutral Terms, Jehad Alzabut, Martin Bohner, Said R. Grace Dec 2021

Oscillation Of Nonlinear Third-Order Difference Equations With Mixed Neutral Terms, Jehad Alzabut, Martin Bohner, Said R. Grace

Mathematics and Statistics Faculty Research & Creative Works

In this paper, new oscillation results for nonlinear third-order difference equations with mixed neutral terms are established. Unlike previously used techniques, which often were based on Riccati transformation and involve limsup or liminf conditions for the oscillation, the main results are obtained by means of a new approach, which is based on a comparison technique. Our new results extend, simplify, and improve existing results in the literature. Two examples with specific values of parameters are offered.

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(R1887) Inferring Trends Of Point Processes From Non-Iid Samples, Bruno Appolloni Dec 2021

(R1887) Inferring Trends Of Point Processes From Non-Iid Samples, Bruno Appolloni

Applications and Applied Mathematics: An International Journal (AAM)

We discuss unprecedented, albeit rudimentary, tools to infer the evolution of a point process where the available samples are both truncated and non independently drawn. To achieve this goal, we lay in an intermediate domain between probability models and fuzzy sets, still maintaining probabilistic features of the employed statistics as the reference KPI of the tools. The overall strategy is to frame the problem within the Algorithmic Inference framework and use a sort of kernel trick to distort the seeds of the observed variable so as to render them an iid sample of a random variable in a proper feature …

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(R1493) Discussion On Stability And Hopf-Bifurcation Of An Infected Prey Under Refuge And Predator, Moulipriya Sarkar, Tapasi Das Dec 2021

(R1493) Discussion On Stability And Hopf-Bifurcation Of An Infected Prey Under Refuge And Predator, Moulipriya Sarkar, Tapasi Das

Applications and Applied Mathematics: An International Journal (AAM)

The paper deals with the case of non-selective predation in a partially infected prey-predator system, where both the susceptible prey and predator follow the law of logistic growth and some preys avoid predation by hiding. The disease-free preys get infected in due course of time by a certain rate. However, the carrying capacity of the predator population is considered proportional to the sum-total of the susceptible and infected prey. The positivity and boundedness of the solutions of the system are studied and the existence of the equilibrium points and stability of the system are analyzed at these points. The effect …

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The Physiological Factors Of Diabetes And Their Effect On The Cognitive And Emotional Functioning In Older Populations: A Secondary Data Analysis, Celeste Anahi Alvidrez Dec 2021

The Physiological Factors Of Diabetes And Their Effect On The Cognitive And Emotional Functioning In Older Populations: A Secondary Data Analysis, Celeste Anahi Alvidrez

Open Access Theses & Dissertations

Background: The rates of Type 2 Diabetes (T2D) have increased over the past 20 years in all age groups. The physiological factors that underlie T2D could have impact on specific brain pathways that support cognitive and emotional functioning. Aims and Objective: The goal of this study was to examine whether older Mexican American individuals with a history of T2D were more likely to develop later cognitive impairment and/or depression. Hypotheses: It was predicted that elderly participants (mean age at time of interview = 87.87 years) with a history of T2D onset prior to age 65, are more likely to have …

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(R1463) On The Central Limit Theorem For Conditional Density Estimator In The Single Functional Index Model, Abbes Rabhi, Nadia Kadiri, Fatima Akkal Dec 2021

(R1463) On The Central Limit Theorem For Conditional Density Estimator In The Single Functional Index Model, Abbes Rabhi, Nadia Kadiri, Fatima Akkal

Applications and Applied Mathematics: An International Journal (AAM)

The main objective of this paper is to investigate the nonparametric estimation of the conditional density of a scalar response variable Y, given the explanatory variable X taking value in a Hilbert space when the sample of observations is considered as an independent random variables with identical distribution (i.i.d.) and are linked with a single functional index structure. First of all, a kernel type estimator for the conditional density function (cond-df) is introduced. Afterwards, the asymptotic properties are stated for a conditional density estimator when the observations are linked with a single-index structure from which we derive an central …

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Comparing Machine Learning Techniques With State-Of-The-Art Parametric Prediction Models For Predicting Soybean Traits, Susweta Ray Dec 2021

Comparing Machine Learning Techniques With State-Of-The-Art Parametric Prediction Models For Predicting Soybean Traits, Susweta Ray

Department of Statistics: Dissertations, Theses, and Student Work

Soybean is a significant source of protein and oil, and also widely used as animal feed. Thus, developing lines that are superior in terms of yield, protein and oil content is important to feed the ever-growing population. As opposed to the high-cost phenotyping, genotyping is both cost and time efficient for breeders while evaluating new lines in different environments (location-year combinations) can be costly. Several Genomic prediction (GP) methods have been developed to use the marker and environment data effectively to predict the yield or other relevant phenotypic traits of crops. Our study compares a conventional GP method (GBLUP), a …

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Comparison Of Statistical Methods For Modeling Count Data With An Application To Length Of Hospital Stay, Gustavo A. Fernandez Dec 2021

Comparison Of Statistical Methods For Modeling Count Data With An Application To Length Of Hospital Stay, Gustavo A. Fernandez

Theses and Dissertations

Hospital length of stay (LOS) is a key indicator of hospital care management efficiency, cost of care, and hospital planning. Therefore, understanding hospital LOS variability is always an important healthcare focus. Hospital LOS data are count data, with discrete and nonnegative values, typically right-skewed, and often exhibiting excessive zeros. Numerous studies have been conducted to model hospital LOS to identify significant predictors contributing to its variability. Many researchers have used linear regression with or without logarithmic transformation of the outcome variable LOS, or logistic regression on a dichotomized LOS. These regression methods usually violate models’ assumptions and are subject …

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Factors Influencing Intent To Take A Covid-19 Test In The United States, Sheila Rutto Dec 2021

Factors Influencing Intent To Take A Covid-19 Test In The United States, Sheila Rutto

Theses and Dissertations

In 2020, COVID-19 became the first pandemic in the world’s history that brought the entire world to an abrupt and unexpected halt. Since the first reported case of the disease to date, the novel coronavirus has been able to wreak havoc in literary every corner of the globe and left an ever-growing number of unprecedented fatalities. The normal way of life has been disrupted, and the level of uncertainty about the end of this pandemic continues to manifest to many. Due to the urgency to bring this pandemic under control, medical officers have been able to recommend actions that people …

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Statistical Modeling, Learning And Computing For Stochastic Dynamics Of Complex Systems, Mohammadmahdi Hajiha Dec 2021

Statistical Modeling, Learning And Computing For Stochastic Dynamics Of Complex Systems, Mohammadmahdi Hajiha

Graduate Theses and Dissertations

With the recent advances in sensor technology, it is much easier to collect and store streams of system operational and environmental (SOE) data. These data can be used as input to model the underlying behavior of complex engineered systems and phenomenons if appropriate algorithms with well-defined assumptions are developed. This dissertation is comprised of the research work to show the applicability of SOE data when fed into proposed tailored algorithms. The first purposes of these algorithms are to estimate and analyze the reliability of a system as elaborated in Chapter 2. This chapter provides the derivation of closed-form expressions that …

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Data-Driven Statin Initiation Evaluation And Optimization For Prediabetes Population, Muhenned A. Abdulsahib Dec 2021

Data-Driven Statin Initiation Evaluation And Optimization For Prediabetes Population, Muhenned A. Abdulsahib

Graduate Theses and Dissertations

This dissertation develops quantitative models to support medical decision making of statininitiation considering the uncertainty in disease progression for prediabetes patients. A mathematical model is built to help medical decision-makers take action of statin initiation under uncertainty in future prediabetes progressions. The association between cholesterol drug use, such as statin, and elevating glucose level attracted considerable amounts of attention in the literature. Statin effects on glucose vary with respect to different levels of glucose. The first chapter of this dissertation introduces the problem and an overview of the tools that will be used to solve it. In the second chapter …

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(R1505) A Note On Large Deviations In Insurance Risk, Stefan Gerhold Dec 2021

(R1505) A Note On Large Deviations In Insurance Risk, Stefan Gerhold

Applications and Applied Mathematics: An International Journal (AAM)

We study large and moderate deviations for an insurance portfolio, with the number of claims tending to infinity, without assuming identically distributed claims. The crucial assumption is that the centered claims are bounded, and that variances are bounded below. From a general large deviations upper bound, we obtain an exponential bound for the probability of the average loss exceeding a threshold. A counterexample shows that a full large deviation principle, including also a lower bound, does not follow from our assumptions. We argue that our assumptions make sense, in particular, for life insurance portfolios and discuss how to apply our …

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Functional Mixed Data Clustering With Fourier Basis Smoothing, Ishmael Amartey Dec 2021

Functional Mixed Data Clustering With Fourier Basis Smoothing, Ishmael Amartey

Electronic Theses and Dissertations

Clustering is an important analytical technique that has proven to affect human life positively through its application in cancer research, market segmentation, city planning etc. In this time of growing technological systems, mixed data has seen another face of longitudinal, directional and functional attributes which is worth paying attention to and analyzing. Previous research works on clustering relied largely on the inverse weight technique and B-spline in smoothing data and assessing the performance of various clustering algorithms. In 1971, Gower proposed a method of clustering for mixed variable types which has been extended to include functional and directional variables by …

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Effect Of Renin-Angiotensin System Inhibitors On Acute Kidney Injury Among Patients Undergoing Cardiac Surgery: A Review And Meta-Analysis, Han Zhou, Jingui Xie, Zhichao Zheng, Oon Cheong Ooi, Haidong Luo Dec 2021

Effect Of Renin-Angiotensin System Inhibitors On Acute Kidney Injury Among Patients Undergoing Cardiac Surgery: A Review And Meta-Analysis, Han Zhou, Jingui Xie, Zhichao Zheng, Oon Cheong Ooi, Haidong Luo

Research Collection Lee Kong Chian School Of Business

Acute kidney injury (AKI) is a frequent complication of cardiac surgery, which can lead to higher mortality and long-term renal function impairment. The effect of perioperative renin-angiotensin system inhibitors (RASi) therapy on AKI incidence in patients undergoing cardiac surgery remains controversial. We reviewed related studies in PubMed, Scopus, and Cochrane Library from inception to February 2020. Two randomized controlled trials and 21 cohort studies were included in the meta-analysis, involving 76,321 participants. The pooled odds ratio and 95% confidence interval were calculated using the DerSimonian and Laird random-effects model. The results showed no significant association between perioperative RASi therapy and …

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Integration Of Blockchain Technology Into Automobiles To Prevent And Study The Causes Of Accidents, John Kim Dec 2021

Integration Of Blockchain Technology Into Automobiles To Prevent And Study The Causes Of Accidents, John Kim

Electronic Theses, Projects, and Dissertations

Automobile collisions occur daily. We now live in an information-driven world, one where technology is quickly evolving. Blockchain technology can change the automotive industry, the safety of the motoring public and its surrounding environment by incorporating this vast array of information. It can place safety and efficiency at the forefront to pedestrians, public establishments, and provide public agencies with pertinent information securely and efficiently. Other industries where Blockchain technology has been effective in are as follows: supply chain management, logistics, and banking. This paper reviews some statistical information regarding automobile collisions, Blockchain technology, Smart Contracts, Smart Cities; assesses the feasibility …

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Predictors Of Poor Glycemic Control In Diabetic Clients With Mental Health Illness, Community Alliance, Omaha, Nebraska, Rachelle Flick Dec 2021

Predictors Of Poor Glycemic Control In Diabetic Clients With Mental Health Illness, Community Alliance, Omaha, Nebraska, Rachelle Flick

Capstone Experience

People with severe mental illness tend to die 10-25 years earlier than the general population (WHO). Main contributors to these premature deaths include comorbidities such as hypertension, cardiovascular disease, and diabetes. Diabetes prevalence in mentally ill people is 2 times higher than the general population (WHO). The World Health Organization is taking action to improve the health of people with severe mental illness. These efforts include creating protocols of prevention, identification, assessment, and treatment for mentally ill people, as well as improving access to general health services through the integration of physical and mental health services. Community Alliance, located in …

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Estimating Treatment Effect On Medical Cost And Examining Medical Cost Trajectory Using Splines And Change Point Techniques., Indranil Ghosh Dec 2021

Estimating Treatment Effect On Medical Cost And Examining Medical Cost Trajectory Using Splines And Change Point Techniques., Indranil Ghosh

Electronic Theses and Dissertations

In the world of growing medical needs, other than the clinical outcomes, the cost of healthcare is one of the important aspects to evaluate. The cost of treatment could act as a decisive factor on which one to choose from two equally likely effective treatment options. In literature, the most used quantity for the cost of treatment is cumulative lifetime cost since the diagnosis of a disease. While it provides a bird' eye view of the treatment cost, it fails to capture the underlying pattern of the treatment cost trajectory. We developed a marginal structural functional model (MSFM) using an …

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A New Algorithm For Robust Affine-Invariant Clustering, Andrews Tawiah Anum Dec 2021

A New Algorithm For Robust Affine-Invariant Clustering, Andrews Tawiah Anum

Open Access Theses & Dissertations

Cluster analysis is an unsupervised machine learning technique commonly employed to partition a dataset into distinct categories referred to as clusters. The k-means algorithm is a prominent distance-based clustering method. Despite its overwhelming popularity, the algorithm is not invariant under non-singular linear transformations and is not robust, i.e., can be unduly influenced by outliers. To address these deficiencies, we propose an alternative clustering procedure based on minimizing a “trimmed” variant of the negative log-likelihood function. We develop a “concentration step”, vaguely reminiscent of the classical Lloyd’s algorithm, that can iteratively reduce the objective function. Multiple real and synthetic datasets are …

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Challenges For Estimating The Global Prevalence Of Micronutrient Deficiencies And Related Disease Burden: A Case Study Of The Global Burden Of Disease Study, Sonja Y. Hess, Alexander C. Mclain Ph.D., Edward A. Frongillo Jr. Ph.D., Ashkan Afshin, Nicholas J. Kassebaum, Saskia Jm Osendarp, Reed Atkin, Rahul Rawat, Kenneth H. Brown Dec 2021

Challenges For Estimating The Global Prevalence Of Micronutrient Deficiencies And Related Disease Burden: A Case Study Of The Global Burden Of Disease Study, Sonja Y. Hess, Alexander C. Mclain Ph.D., Edward A. Frongillo Jr. Ph.D., Ashkan Afshin, Nicholas J. Kassebaum, Saskia Jm Osendarp, Reed Atkin, Rahul Rawat, Kenneth H. Brown

Faculty Publications

Information on the prevalence of micronutrient deficiencies is needed to determine related disease burden; underpin evidence-based advocacy; and design, deliver, and monitor safe, effective interventions. Assessing the global prevalence of deficiency requires a valid micronutrient status biomarker with an appropriate cutoff to define deficiency and relevant data from representative surveys across multiple locations and years. The Global Burden of Disease Study includes prevalence estimates for iodine, iron, zinc, and vitamin A deficiencies, for which recommended biomarkers and appropriate deficiency cutoffs exist. Because representative survey data are lacking, only retinol concentration is used to model vitamin A deficiency, and proxy indicators …

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Gps-Denied Navigation Using Synthetic Aperture Radar Images And Neural Networks, Teresa White Dec 2021

Gps-Denied Navigation Using Synthetic Aperture Radar Images And Neural Networks, Teresa White

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Unmanned aerial vehicles (UAV) often rely on GPS for navigation. GPS signals, however, are very low in power and easily jammed or otherwise disrupted. This paper presents a method for determining the navigation errors present at the beginning of a GPS-denied period utilizing data from a synthetic aperture radar (SAR) system. This is accomplished by comparing an online-generated SAR image with a reference image obtained a priori. The distortions relative to the reference image are learned and exploited with a convolutional neural network to recover the initial navigational errors, which can be used to recover the true flight trajectory throughout …

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Risk-Based Machine Learning Approaches For Probabilistic Transient Stability, Umair Shahzad Dec 2021

Risk-Based Machine Learning Approaches For Probabilistic Transient Stability, Umair Shahzad

Department of Electrical and Computer Engineering: Dissertations, Theses, and Student Research

Power systems are getting more complex than ever and are consequently operating close to their limit of stability. Moreover, with the increasing demand of renewable wind generation, and the requirement to maintain a secure power system, the importance of transient stability cannot be overestimated. Considering its significance in power system security, it is important to propose a different approach for enhancing the transient stability, considering uncertainties. Current deterministic industry practices of transient stability assessment ignore the probabilistic nature of variables (fault type, fault location, fault clearing time, etc.). These approaches typically provide a conservative criterion and can result in expensive …

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An Alternative Class Of Ratio-Regression-Type Estimator Under Two-Phase Sampling Scheme, Muhammad Isah, Zakari Yahaya, Audu Ahmed Dec 2021

An Alternative Class Of Ratio-Regression-Type Estimator Under Two-Phase Sampling Scheme, Muhammad Isah, Zakari Yahaya, Audu Ahmed

CBN Journal of Applied Statistics (JAS)

In this study, a new exponential ratio-regression estimator is developed using an auxiliary variable for estimating the finite population mean under a two-phase sampling system. The Bias and Mean Square Error (MSE) of the proposed estimator are derived and compared with some of the estimators in extant literature. Thus, the conditions under which the proposed estimator is better than some existing estimators are provided. Empirically, using four real datasets and simulation study, the proposed estimator performs better than the classical ratio, classical regression, exponential ratio, and exponential regression cum ratio estimator when compared using the criteria of bias, mean square …

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Confidence Interval For The Mean Of A Beta Distribution, Sean Rangel Dec 2021

Confidence Interval For The Mean Of A Beta Distribution, Sean Rangel

Electronic Theses and Dissertations

Statistical inference for the mean of a beta distribution has become increasingly popular in various fields of academic research. In this study, we developed a novel statistical model from likelihood-based techniques to evaluate various confidence interval techniques for the mean of a beta distribution. Simulation studies will be implemented to compare the performance of the confidence intervals. In addition to the development and study involving confidence intervals, we will also apply the confidence intervals to real biological data that was gathered by the Department of Biology at Stephen F. Austin State University and provide recommendations on the best practice.

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A Copula Model Approach To Identify The Differential Gene Expression, Prasansha Liyanaarachchi Dec 2021

A Copula Model Approach To Identify The Differential Gene Expression, Prasansha Liyanaarachchi

Mathematics & Statistics Theses & Dissertations

Deoxyribonucleic acid, more commonly known as DNA, is a complex double helix-shaped molecule present in all living organisms and hosts thousands of genes. However, only a few genes exhibit differential expression and play a vital role in a particular disease such as breast cancer. Microarray technology is one of the modern technologies developed to study these gene expressions. There are two major microarray technologies available for expression analysis: Spotted cDNA array and oligonucleotide array. The focus of our research is the statistical analysis of data that arises from the spotted cDNA microarray. Numerous models have been proposed in the literature …

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Statistical Analysis Based On Adaptive Progressive Hybrid Censored Data From Lomax Distribution, Amal Helu, Hani Samawi Nov 2021

Statistical Analysis Based On Adaptive Progressive Hybrid Censored Data From Lomax Distribution, Amal Helu, Hani Samawi

Department of Biostatistics, Epidemiology, and Environmental Health Sciences Faculty Publications

In this article, we consider statistical inferences about the unknown parameters of the Lomax distribution basedon the Adaptive Type-II Progressive Hybrid censoring scheme, this scheme can save both the total test time and the cost induced by the failure of the units and increases the efficiency of statistical analysis. The estimation of the parameters is derived using the maximum likelihood (MLE) and the Bayesian procedures. The Bayesian estimators are obtained based on the symmetric and asymmetric loss functions. There are no explicit forms for the Bayesian estimators, therefore, we propose Lindley’s approximation method to compute the Bayesian estimators. A comparison …

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