Statistics and Probability Commons^™

A New Right-Skewed Upside Down Bathtub Shaped Heavy-Tailed Distribution And Its Applications, Sandeep Kumar Maurya, Sanjay K. Singh, Umesh Singh

Journal of Modern Applied Statistical Methods

A one parameter right skewed, upside down bathtub type, heavy-tailed distribution is derived. Various statistical properties and maximum likelihood approaches for estimation purpose are studied. Five different real data sets with four different models are considered to illustrate the suitability of the proposed model.

On The Level Of Precision Of A Heterogeneous Transfer Function In A Statistical Neural Network Model, Christopher Godwin Udomboso

Journal of Modern Applied Statistical Methods

A heterogeneous function of the statistical neural network is presented from two transfer functions: symmetric saturated linear and hyperbolic tangent sigmoid. The precision of the derived heterogeneous model over their respective homogeneous forms are established, both at increased sample sizes hidden neurons. Results further show the sensitivity of the heterogeneous model to increase in hidden neurons.

A New Generalized Family Of Distributions For Lifetime Data, Maha A. D. Aldahlan, Mohamed G. Khalil, Ahmed Z. Afify

Journal of Modern Applied Statistical Methods

A new class of continuous distributions called the generalized Burr X-G family is introduced. Some special models of the new family are provided. Some of its mathematical properties including explicit expressions for the quantile and generating functions, ordinary and incomplete moments, order statistics and Rényi entropy are derived. The maximum likelihood is used for estimating the model parameters. The flexibility of the generated family is illustrated by means of two applications to real data sets.

Jmasm 57: Bayesian Survival Analysis Of Lomax Family Models With Stan (R), Mohammed H. A. Abujarad, Athar Ali Khan

Journal of Modern Applied Statistical Methods

An attempt is made to fit three distributions, the Lomax, exponential Lomax, and Weibull Lomax to implement Bayesian methods to analyze Myeloma patients using Stan. This model is applied to a real survival censored data so that all the concepts and computations will be around the same data. A code was developed and improved to implement censored mechanism throughout using rstan. Furthermore, parallel simulation tools are also implemented with an extensive use of rstan.

Vif-Regression Screening Ultrahigh Dimensional Feature Space, Hassan S. Uraibi

Journal of Modern Applied Statistical Methods

Iterative Sure Independent Screening (ISIS) was proposed for the problem of variable selection with ultrahigh dimensional feature space. Unfortunately, the ISIS method transforms the dimensionality of features from ultrahigh to ultra-low and may result in un-reliable inference when the number of important variables particularly is greater than the screening threshold. The proposed method has transformed the ultrahigh dimensionality of features to high dimension space in order to remedy of losing some information by ISIS method. The proposed method is compared with ISIS method by using real data and simulation. The results show this method is more efficient and more reliable …

A Simple Random Sampling Modified Dual To Product Estimator For Estimating Population Mean Using Order Statistics, Sanjay Kumar, Priyanka Chhaparwal

Journal of Modern Applied Statistical Methods

Bandopadhyaya (1980) developed a dual to product estimator using robust modified maximum likelihood estimators (MMLE’s). Their properties were obtained theoretically and supported through simulations studies with generated as well as one real data set. Robustness properties in the presence of outliers and confidence intervals were studied.

Penalized Likelihood Estimation Of Gamma Distributed Response Variable Via Corrected Solution Of Regression Coefficients, Rasaki Olawale Olanrewaju

Journal of Modern Applied Statistical Methods

A Gamma distributed response is subjected to regression penalized likelihood estimations of Least Absolute Shrinkage and Selection Operator (LASSO) and Minimax Concave Penalty via Generalized Linear Models (GLMs). The Gamma related disturbance controls the influence of skewness and spread in the corrected path solutions of the regression coefficients.

Inference For Step-Stress Partially Accelerated Life Test Model With An Adaptive Type-I Progressively Hybrid Censored Data, Showkat Ahmad Lone, Ahmadur Rahman, Tanveer A. Tarray

Journal of Modern Applied Statistical Methods

Consider estimating data of failure times under step-stress partially accelerated life tests based on adaptive Type-I hybrid censoring. The mathematical model related to the lifetime of the test units is assumed to follow Rayleigh distribution. The point and interval maximum-likelihood estimations are obtained for distribution parameter and tampering coefficient. Also, the work is conducted under a traditional Type-I hybrid censoring plan (scheme). A Monte Carlo simulation algorithm is used to evaluate and compare the performances of the estimators of the tempering coefficient and model parameters under both progressively hybrid censoring plans. The comparison is carried out on the basis of …

Data-Driven Analytical Modeling Of Multiple Myeloma Cancer, U.S. Crop Production And Monitoring Process, Lohuwa Mamudu

USF Tampa Graduate Theses and Dissertations

Globally, cancer disease is a major health issue causing a lot of deaths. The duration of time an individual diagnosed with a particular type of cancer survives has become a major area of research concern. The Kaplan Meier and Cox Proportional Hazard (Cox-PH) model have been a traditionally used method for survival analysis of cancer data. These techniques of cancer survival analysis are developed from nonparametric and semi-parametric approaches, respectively, which are not as robust as a parametric approach. In this dissertation, we proposed a new method of cancer survival analysis based on a parametric approach using multiple myeloma cancer …

Fully Bayesian Analysis Of Relevance Vector Machine Classification With Probit Link Function For Imbalanced Data Problem, Wenyang Wang, Dongchu Sun, Peng Shao, Haibo Kuang, Cong Sui

Department of Statistics: Faculty Publications

The original RVM classification model uses the logistic link function to build the likelihood function making the model hard to be conducted since the posterior of the weight parameter has no closed-form solution. This article proposes the probit link function approach instead of the logistic one for the likelihood function in the RVM classification model, namely PRVM (RVM with the probit link function). We show that the posterior of the weight parameter in PRVM follows the Multivariate Normal distribution and achieves a closed-form solution. A latent variable is needed in our algorithms to simplify the Bayesian computation greatly, and its …

Efficient, Positive, And Energy Stable Schemes For Multi-D Poisson–Nernst–Planck Systems, Hailiang Liu, Wumaier Maimaitiyiming

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we design, analyze, and numerically validate positive and energy-dissipating schemes for solving the time-dependent multi-dimensional system of Poisson–Nernst–Planck equations, which has found much use in the modeling of biological membrane channels and semiconductor devices. The semi-implicit time discretization based on a reformulation of the system gives a well-posed elliptic system, which is shown to preserve solution positivity for arbitrary time steps. The first order (in time) fully discrete scheme is shown to preserve solution positivity and mass conservation unconditionally, and energy dissipation with only a mild O (1) time step restriction. The scheme is also shown to …

Weighted Geometric Mean And Its Properties, Ievgen Turchyn

Applications and Applied Mathematics: An International Journal (AAM)

Various means (the arithmetic mean, the geometric mean, the harmonic mean, the power means) are often used as central tendency statistics. A new statistic of such type is offered for a sample from a distribution on the positive semi-axis, the γ-weighted geometric mean. This statistic is a certain weighted geometric mean with adaptive weights. Monte Carlo simulations showed that the γ-weighted geometric mean possesses low variance: smaller than the variance of the 0.20-trimmed mean for the Lomax distribution. The bias of the new statistic was also studied. We studied the bias in terms of nonparametric confidence intervals for the quantiles …

Analysis Of Means (Anom) Concepts And Computations, Kalanka P. Jayalath, Jacob Turner

Applications and Applied Mathematics: An International Journal (AAM)

The classical Analysis of Means (ANOM) is a statistical inferencing procedure and visualization tool to analyze means from experiments with fixed effects. It can serve as an alternative to the Analysis of Variance (ANOVA) procedure that has distinct advantages when determining which effects contributed to an overall test’s significant result. ANOM has been extended to handle numerous situations including robust procedures involving ranks. More recent advancements of this procedure allow one to handle both random, and mixed effect models. In this work, we discuss the recent developments on ANOM methods that are useful in practice, provide examples that illustrate their …

Some Asymptotic Properties Of Conditional Density Function For Functional Data Under Random Censorship, Fatima Akkal, Abbes Rabhi, Latifa Keddani

Applications and Applied Mathematics: An International Journal (AAM)

In this work, we investigate the asymptotic properties of a nonparametric mode of a conditional density when the real response variable is censored and the explanatory variable is valued in a semi- metric space under ergodic data. First of all, we establish asymptotic properties for a conditional density estimator from which we derive an central limit theorem (CLT) of the conditional mode estimator. Simulation study is also presented to illustrate the validity and finite sample performance of the considered estimator.

Pivot Points In Bivariate Linear Regression, David L. Farnsworth, Carl V. Lutzer

Articles

There are little-noticed points in the plane, which are artifacts of linear regression. The points, which are called pivot points, are the intersections of sets of regression lines. We derive the coordinates of the pivot point and explain its sources. We show how a pivot point arises in a certain notable data set, which has been analyzed often for points of high leverage. We obtain the application of pivot points that shortens calculations when updating a set of bivariate observations by adding a new point.

Statistically Defensible Wind Tunnel Models, Timothy A. Roche

Theses and Dissertations

Wind tunnels are used to test scale-model air frames in order to collect aerodynamic data. The Subsonic Aerodynamic Research Laboratory (SARL) Wind Tunnel is a low speed wind tunnel located at Wright-Patterson Air Force Base. The SARL Wind Tunnel team approached AFIT for assistance in creating statistically defensible models for the conditions inside the wind tunnel. During a wind tunnel test, pressure sensors cannot be placed at the test model. Instead, pressure is measured by a pitot probe permanently mounted in the corner of the test chamber. The pressure at the model location is predicted from the measurements taken by …

Nonparametric Relative Error Estimation Via Functional Regressor By The K Nearest Neighbors Smoothing Under Truncation Random Data, Wahiba Bouabsa

Applications and Applied Mathematics: An International Journal (AAM)

The relation between a functional random covariate and a scalar answer due to left truncation by a different random variable is evaluated in this study with the kNN method. In particular, in order to produce a nonparametric kNN regression operator of these functional truncated data as a loss function, we should use mean squared relative error. In number of neighbors, we establish an estimator and assess the uniform consistency performance with the convergence rate. Then, for different levels of computational truncated data, a simulation analysis was carried out on finite-sized samples to show the feasibility of our estimation procedure and …

Theoretical Study Of Mach Number And Compressibility Effect On The Slender Airfoils, Abrar Hoque, Masudar Rahman, Ashabul Hoque

Applications and Applied Mathematics: An International Journal (AAM)

Theoretical development of the velocity potential equation for compressible flow and its various consequences has been presented. The geometrical interpretation of potential equation and conformal mapping technique are discussed where the mappings link the flow around a circular cylinder of a slender airfoil. The lift and drag coefficients are determined for the slender airfoils based on the Mach number and compressibility effects. The calculated lift coefficients show that with the increasing of attack angle it increases linearly and a higher lift coefficient is found for a smaller Mach number for any certain attack angle. Similarly, the drag profiles are determined …

Generation And Statistical Properties For Lindley-Polynomial Distribution, Dariush Ghorbanzadeh

Applications and Applied Mathematics: An International Journal (AAM)

For the modeling of the wind speed, we propose a family of distributions in polynomial form generating the Lindley distribution. We call this distribution Lindley-Polynomial distribution. The estimation of parameters using the maximum product spacing estimation method. A real data set has been considered to illustrate the practical utility of the paper.

On Burr Iii-Inverse Weibull Distribution With Covid-19 Applications, Fiaz Ahmad Bhatti, Sedigheh Mirzaei Salehabadi, Gholamhossein G. Hamedani

Mathematical and Statistical Science Faculty Research and Publications

We introduce a flexible lifetime distribution called Burr III-Inverse Weibull (BIII-IW). The new proposed distribution has well-known sub-models. The BIII-IW density function includes exponential, left-skewed, right-skewed and symmetrical shapes. The BIII-IW model’s failure rate can be monotone and non-monotone depending on the parameter values. To show the importance of the BIII-IW distribution, we establish various mathematical properties such as random number generator, ordinary moments, conditional moments, residual life functions, reliability measures and characterizations. We address the maximum likelihood estimates (MLE) for the BIII-IW parameters and estimate the precision of the maximum likelihood estimators via a simulation study. We consider applications …

Nonparametric Estimation Of The Conditional Distribution Function For Surrogate Data By The Regression Model, Imane Metmous, Mohammed K. Attouch, Boubaker Mechab, Torkia Merouan

Applications and Applied Mathematics: An International Journal (AAM)

The main objective of this paper is to estimate the conditional cumulative distribution using the nonparametric kernel method for a surrogated scalar response variable given a functional random one. We introduce the new kernel type estimator for the conditional cumulative distribution function (cond-cdf) of this kind of data. Afterward, we estimate the quantile by inverting this estimated cond-cdf and state the asymptotic properties. The uniform almost complete convergence (with rate) of the kernel estimate of this model and the quantile estimator is established. Finally, a simulation study completed to show how our methodology can be adopted.

Data Analysis And Visualization To Dismantle Gender Discrimination In The Field Of Technology, Quinn Bolewicki

Dissertations, Theses, and Capstone Projects

In the United States, a significant population is facing an uphill battle trying to thrive in an industry that has seen exponential growth in recent years. Women, who account for approximately 50.8% of the U.S. population are statistically underpaid and underrepresented in science, technology, engineering, and mathematics (STEM). Despite women-led technology teams establishing a 21% greater return on investment than teams who don’t, and young women largely outperforming men in math according to a 2015 study, there are only three fortune 500 companies led by women, and they comprise only 10% of internet entrepreneurs. Research generates hundreds of articles, infographics, …

A Geometric Approach To Conditioning And The Search For Minimum Variance Unbiased Estimators, David L. Farnsworth, James E. Marengo

Articles

Our purpose is twofold: to present a prototypical example of the conditioning technique to obtain the best estimator of a parameter and to show that this technique resides in the structure of an inner product space. The technique uses conditioning of an unbiased estimator on a sufficient statistic. This procedure is founded upon the conditional variance formula, which leads to an inner product space and a geometric interpretation. The example clearly illustrates the dependence on the sampling methodology. These advantages show the power and centrality of this process.

Modeling And Solving The Outsourcing Risk Management Problem In Multi-Echelon Supply Chains, Arian A. Nahangi

Master's Theses

Worldwide globalization has made supply chains more vulnerable to risk factors, increasing the associated costs of outsourcing goods. Outsourcing is highly beneficial for any company that values building upon its core competencies, but the emergence of the COVID-19 pandemic and other crises have exposed significant vulnerabilities within supply chains. These disruptions forced a shift in the production of goods from outsourcing to domestic methods.

This paper considers a multi-echelon supply chain model with global and domestic raw material suppliers, manufacturing plants, warehouses, and markets. All levels within the supply chain network are evaluated from a holistic perspective, calculating a total …

Asymmetric Multivariate Archimedean Copula Models And Semi-Competing Risks Data Analysis, Ziyan Guo

Dissertations

Many multivariate models have been proposed and developed to model high dimensional data when the dimension of a data set is greater than 2 (d ≥ 3). The existing multivariate models often force the “exchangeable” structure for part or the whole model, are not very flexible which tends to be of limited use in practice. There is a demand for developing and studying multivariate models with any pre-specified bivariate margins.

Suppose there exists such a class of flexible models with any pre-specified bivariate margins. Given a multivariate data, what is the distribution function and how to easily estimate the parameters …

Convolutional Neural Networks For Deflate Data Encoding Classification Of High Entropy File Fragments, Nehal Ameen

LSU New Orleans Theses and Dissertations

Data reconstruction is significantly improved in terms of speed and accuracy by reliable data encoding fragment classification. To date, work on this problem has been successful with file structures of low entropy that contain sparse data, such as large tables or logs. Classifying compressed, encrypted, and random data that exhibit high entropy is an inherently difficult problem that requires more advanced classification approaches. We explore the ability of convolutional neural networks and word embeddings to classify deflate data encoding of high entropy file fragments after establishing ground truth using controlled datasets. Our model is designed to either successfully classify file …

Machine Learning Based Restaurant Sales Forecasting, Austin B. Schmidt

LSU New Orleans Theses and Dissertations

To encourage proper employee scheduling for managing crew load, restaurants have a need for accurate sales forecasting. We predict partitions of sales days, so each day is broken up into three sales periods: 10:00 AM-1:59 PM, 2:00 PM-5:59 PM, and 6:00 PM-10:00 PM. This study focuses on the middle timeslot, where sales forecasts should extend for one week. We gather three years of sales between 2016-2019 from a local restaurant, to generate a new dataset for researching sales forecasting methods.

Outlined are methodologies used when going from raw data to a workable dataset. We test many machine learning models on …

Dimensionless Analysis Of Trajectories Of Cylindrical Objects Dropped Into Water In Two Dimensions, Yi Zhen

LSU New Orleans Theses and Dissertations

Nondimensionalization is powerful technique and is widely applied in the study of fluid mechanics and engineering because it 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 phenomena. The nondimensionalization of 2D theory has been completed by the author (Zhen et.al.,2020) and new dimensionless equations of motion were obtained. In this study, new dimensionless dynamic equations are extended by incorporating new parameters to cope with various environmental conditions. The new dimensionless analysis of dropped cylindrical objects is consisted of four parts.

Part 1, …

The Essence Of Telemedicine For Bridging The Gap In Health Services, Budi Wiweko, Sarah Chairani Zakirah, Atha Luthfi

Kesmas

This study aimed to review the essence of telemedicine in this modern era of technology and innovation, especially in developing countries. It also investigated the regulation aspect as the main component for healthcare services. There were five main categories of telemedicine: revenue stream and technology literacy, health facilities, human resources, data authorization and security, and health protocol. Furthermore, when combined with wearable devices, it enhanced healthcare delivery opportunities. There were two major components of global electronic health, namely telehealth and health informatics, based one-commerce and e-learning systems. The World Health Organization (WHO) has been able to describe the roles of …

The Determinants Of Stunting For Children Aged 24-59 Months In Kulon Progo District 2019, Chatrine Aprilia Hendraswari, Yuliasti Eka Purnamaningrum, Tri Maryani, Yani Widyastuti, Sakinah Harith

Kesmas

This study pertains to stunting in children in Indonesian with z-scores of less than -2 Standard Deviation (SD) and less than -3 SD. The preliminary study results showed the highest prevalence of stunting to be 22.6%, at the Temon II Primary Health Care in Kulon Progo District. The study aimed to assess the determinants of stunting children aged 24–59 months. This study was conducted from September 2018–May 2019. The design of this study was analytical observational with study design case-control. The sample was 60 children aged 24–59 months. The method utilized proportional sampling, whereas the data analysis applied chi-square and …