Statistics and Probability Commons^™

Surface Reconstruction Using Differential Invariant Signatures, Sophors Khut

Mathematics, Statistics, and Computer Science Honors Projects

This thesis addresses the problem of reassembling a broken surface. Three di- mensional curve matching is used to determine shared edges of broken pieces. In practice, these pieces may have different orientation and position in space, so edges cannot be directly compared. Instead, a differential invariant signature is used to make the comparison. A similarity score between edge signatures determines if two pieces share an edge. The Procrustes algorithm is applied to find the translations and rotations that best fit shared edges. The method is implemented in Matlab, and tested on a broken spherical surface.

Hurdle Models And Age Effects In The Major League Baseball Draft, Justin Sims

Mathematics, Statistics, and Computer Science Honors Projects

Major League Baseball (MLB) franchises expend an abundance of resources on scouting in preparation for the June Amateur Draft. In addition to the classic "tools" assessed, another factor considered is age: younger players may get selected over older players of equal ability because of anticipated development, whereas college players may get selected over high school players due to a shortened latency before reaching the majors. Additionally, Little League rules in effect until 2006 operated on an August 1-July 31 year, meaning that, in their youth, players born on August 1 were the eldest relative to their cohort. We examine the …

Parallel Design Patterns And Program Performance, Yu Zhao

Mathematics, Statistics, and Computer Science Honors Projects

With the rapid advancement of parallel and distributed computing (PDC), three types of hardware and their corresponding software (hardware-software pairs) are becoming more and more popular: Distributed Memory Systems with the Message Passing Interface (MPI) library, Shared Memory Systems with the OpenMP library and Co-processor Systems with a general purpose parallel computing library. Alongside the development of both hardware and software aspects of PDC, the process of designing parallel programs has also improved significantly over the years. A consequence of this is that researchers have been able to describe many parallel design patterns, which are recurring solutions to well-known problems …

Bias And Precision Of The Squared Canonical Correlation Coefficient Under Nonnormal Data Condition, Lesley F. Leach, Robin K. Henson

Journal of Modern Applied Statistical Methods

Monte Carlo methods were employed to investigate the effect of nonnormality on the bias associated with the squared canonical correlation coefficient (R_c²). The majority of R_c² estimates were found to be extremely biased, but the magnitude of bias was impacted little by the degree of nonnormality.

Stochastic Randomized Response Model For A Quantitative Sensitive Random Variable, Sarjinder Singh, Stephen A. Sedory

Journal of Modern Applied Statistical Methods

A new stochastic randomized response model is introduced that is useful for estimating the population mean of a sensitive quantitative variable. The proposed stochastic randomized response model is an extension of the stochastic randomized response model from a qualitative sensitive variable to a quantitative variable found in Singh (2002). The stochastic nature of a randomized response device helps increase a respondent’s cooperation while collecting information on sensitive variables in a society. The Bar-Lev, Bobovitch, and Boukai (2004) model is shown to be a special case of the proposed model.

Ridge Regression In Calibration Models With Symmetric Padding Extension-Daubechies Wavelet Transform Preprocessing, Nurwiani, S Sunaryo, Setiawan, B W. Otok

Journal of Modern Applied Statistical Methods

Wavelet transformation is commonly used in calibration models as a preprocessing step. This preprocessing does not involve all results of a spectrum discretization; consequently, a lot of information can be missing. To avoid missing information, a symmetric padding extension (SPE) can be used to place all data points into dyadic scales, however, high dimensional discretization points need to be reduced. Dimension reduction can be performed with Daubechies wavelet transformation (DWT). Scale function and Daubechies wavelet are continuous functions, thus they perform a faster approximation. SPE-DWT preprocessing combines SPE and DWT. Multicollinearity often occurs in calibration models; the ridge regression (RR) …

Statistical Power Of Alternative Structural Models For Comparative Effectiveness Research: Advantages Of Modeling Unreliability, Emil N. Coman, Eugen Iordache, Lisa Dierker, Judith Fifield, Jean J. Schensul, Suzanne Suggs, Russell Barbour

Journal of Modern Applied Statistical Methods

The advantages of modeling the unreliability of outcomes when evaluating the comparative effectiveness of health interventions is illustrated. Adding an action-research intervention component to a regular summer job program for youth was expected to help in preventing risk behaviors. A series of simple two-group alternative structural equation models are compared to test the effect of the intervention on one key attitudinal outcome in terms of model fit and statistical power with Monte Carlo simulations. Some models presuming parameters equal across the intervention and comparison groups were under- powered to detect the intervention effect, yet modeling the unreliability of the outcome …

A Flexible Method For Conducting Power Analysis For Two- And Three-Level Hierarchical Linear Models In R, Yi Pan, Matthew T. Mcbee

Journal of Modern Applied Statistical Methods

A general approach for conducting power analysis in two- and three-level hierarchical linear models (HLMs) is described. The method can be used to perform power analysis to detect fixed effects at any level of a HLM with dichotomous or continuous covariates. It can easily be extended to perform power analysis for functions of parameters. Important steps in the derivation of this approach are illustrated and numerical examples are provided. Sample code implementing this approach is provided using the free program R.

Estimation Of Reliability In Multicomponent Stress-Strength Based On Generalized Rayleigh Distribution, Gadde Srinivasa Rao

Journal of Modern Applied Statistical Methods

A multicomponent system of k components having strengths following k- independently and identically distributed random variables x₁, x₂, ..., x_k and each component experiencing a random stress Y is considered. The system is regarded as alive only if at least s out of k (s < k) strengths exceed the stress. The reliability of such a system is obtained when strength and stress variates are given by a generalized Rayleigh distribution with different shape parameters. Reliability is estimated using the maximum likelihood (ML) method of estimation in samples drawn from strength and stress …

Specifying Asymmetric Star Models With Linear And Nonlinear Garch Innovations: Monte Carlo Approach, Olaoluwa S. Yaya, Olanrewaju I. Shittu

Journal of Modern Applied Statistical Methods

Economic and finance time series are typically asymmetric and are expected to be modeled using asymmetrical nonlinear time series models. Smooth Transition Autoregressive (STAR) models: Logistic (LSTAR) and Exponential (ESTAR) are known to be asymmetric and symmetric respectively. Under non-normal and heteroscedastic innovations, the residuals of these models are estimated using Generalized Autoregressive Conditionally Heteroscedastic (GARCH) models with variants which include linear and nonlinear forms. The small sample properties of STAR-GARCH variants are yet to be established but these properties are investigated using Monte Carlo (MC) simulation. An MC investigation was conducted to investigate the performance of selections of STAR-GARCH …

Robustness Of Several Estimators Of The Acf Of Ar(1) Process With Non-Gaussian Errors, A A. Smadi, J J. Jaber, A G. Al-Zu'bi

Journal of Modern Applied Statistical Methods

The autocorrelation function (ACF) plays an important role in the context of ARMA modeling, especially for their identification and estimation. This study considers the robust estimation of the ACF of the AR(1) model if the white noise (WN) process is non- Gaussian. Three estimators including the ordinary moment estimator and two other (robust) estimators are considered. The impacts of the deviation from normality of the WN process on those estimators in terms of bias, MSE and distribution via Monte-Carlo simulation are examined. The empirical distribution of those estimators when the errors are normal, t, Cauchy and exponential are studied. …

Two Parameter Modified Ratio Estimators With Two Auxiliary Variables For Estimation Of Finite Population Mean With Known Skewness, Kurtosis And Correlation Coefficient, Jambulingam Subramani, G Prabavathy

Journal of Modern Applied Statistical Methods

Consider the two parameter modified ratio estimators for the estimation of finite population mean using the skewness, kurtosis and correlation coefficient of two auxiliary variables. The efficiencies of the proposed modified ratio estimators are assessed with that of the simple random sampling without replacement (SRSWOR) sample mean and some of the existing ratio estimators in terms of mean squared errors. The entire above is explained with the help of certain natural populations available in the literature.

Change Point Estimation For Pareto Type-Ii Model, Gyan Prakash

Journal of Modern Applied Statistical Methods

Some Bayes estimators of the change point for the Pareto Type-II model under right item failure-censoring scheme are proposed. The Bayes estimators are obtained here in two cases, the first is when one parameter is known and second when both parameters are considered as the random variable. The performances of the procedures are illustrated by simulation technique.

Comparison Of Three Calculation Methods For A Bayesian Inference Of Two Poisson Parameters, Yohei Kawasaki, Etsuo Miyaoka

Journal of Modern Applied Statistical Methods

The statistical inference drawn from the difference between two independent Poisson parameters is often discussed in medical literature. Kawasaki and Miyaoka (2012) proposed an index θ = P(λ_1,post < λ_2,post), where λ_1,post and λ_2,post denote Poisson parameters following posterior density. A new calculation method is proposed using MCMC and an approximate expression and exact expression for θ are compared.

Likelihood Ratio Type Test For Linear Failure Rate Distribution Vs. Exponential Distribution, R R. L. Kantam, M C. Priya, M S. Ravikumar

Journal of Modern Applied Statistical Methods

The Linear Failure Rate Distribution (LFRD) is considered. The graphs of its probability density function are examined for selected parameter combinations. Some of them are similar to the well-known exponential distribution. Incidentally exponential distribution is one of the two component models of the LFRD model. In view of the simpler form of exponential model as applicable in inference, looking at the frequency curves of LFRD, a test statistic is proposed based on ratio of likelihood functions containing the standard forms of the density functions of both LFRD and Exponential to discriminate between LFRD and exponential models. The critical values and …

A Comparison Of Shape And Scale Estimators Of The Two-Parameter Weibull Distribution, Florence George

Journal of Modern Applied Statistical Methods

Weibull distributions are widely used in reliability and survival analysis. In this paper, different methods to estimate the shape and scale parameters of the two-parameter Weibull distribution have been reviewed and compared, based on the bias, mean square error and variance. Because a theoretical comparison is not possible, an extensive simulation study has been conducted to compare the performance of different estimators. Based on the simulation study it was observed that MLE consistently performs better than other methods.

An Alternative Test For The Equality Of Intraclass Correlation Coefficients Under Unequal Family Sizes For Several Populations, Madhusudan Bhandary, Koji Fujiwara

Journal of Modern Applied Statistical Methods

An alternative test for the equality of several intraclass correlation coefficients under unequal family sizes based on several independent multinormal samples is proposed. It was found that the alternative test consistently and reliably produced results superior to those of Likelihood ratio test (LRT) proposed by Bhandary and Alam (2000) and F_max test proposed by Bhandary and Fujiwara (2006) in terms of power for various combinations of intraclass correlation coefficient values and also the alternative test stays closer to the significance level under null hypothesis compared to the Likelihood ratio test and F_max test. This alternative test is computationally …

Inference For The Rayleigh Distribution Based On Progressive Type-Ii Fuzzy Censored Data, Abbas Pak, Gholam Ali Parham, Mansour Saraj

Journal of Modern Applied Statistical Methods

Classical statistical analysis of the Rayleigh distribution deals with precise information. However, in real world situations, experimental performance results cannot always be recorded or measured precisely, but each observable event may only be identified with a fuzzy subset of the sample space. Therefore, the conventional procedures used for estimating the Rayleigh distribution parameter will need to be adapted to the new situation. This article discusses different estimation methods for the parameters of the Rayleigh distribution on the basis of a progressively type-II censoring scheme when the available observations are described by means of fuzzy information. They include the maximum likelihood …

Distance Correlation Coefficient: An Application With Bayesian Approach In Clinical Data Analysis, Atanu Bhattacharjee

Journal of Modern Applied Statistical Methods

The distance correlation coefficient – based on the product-moment approach – is one method by which to explore the relationship between variables. The Bayesian approach is a powerful tool to determine statistical inferences with credible intervals. Prior information about the relationship between BP and Serum cholesterol was applied to formulate the distance correlation between the two variables. The conjugate prior is considered to formulate the posterior estimates of the distance correlations. The illustrated method is simple and is suitable for other experimental studies.

Oscillation Theorems For Fourth-Order Half-Linear Delay Dynamic Equations With Damping, Ravi P. Agarwal, Martin Bohner, Tongxing Li, Chenghui Zhang

Mathematics and Statistics Faculty Research & Creative Works

This article is concerned with oscillatory behavior of a class of fourth-order half-linear delay dynamic equations with damping on a time scale. Some new oscillation criteria are established. © 2013 Springer Basel.

A Comparison Of Prenatal Alcohol, Tobacco, And Other Drug Use Between San Luis Obispo County And Ventura County, Dana M. Williamson

Statistics

Prenatal substance abuse is a growing issue in America. It can lead to fetal alcohol spectrum disorder, long term growth, behavior, and executive functioning problems, and creates a predisposition for drug use for the child.

This project summarizes the statistical analyses comparing alcohol, tobacco, and other drug use by pregnant women between San Luis Obispo County and Ventura County. The main goal of these analyses is to determine if there is a difference between San Luis Obispo County and Ventura County. This is an interesting comparison because these counties are neighboring counties, and past data have shown that the rate …

Patient Rule Induction Method For Subgroup Identification Given Censored Data., Patrick James Trainor

Electronic Theses and Dissertations

The identification of subgroups in clinical studies is an important aspect of personalized medicine. In order to develop tailored therapeutics, the factors that characterize subgroups with differential prognosis, response to treatment, and incidence of adverse events or toxicities must be elucidated. We present a generalization of a statistical learning algorithm, Patient Rule Induction Method (PRIM), that is well suited for this task given a right-censored time-to-event outcome measure. This algorithm works to recursively partition a covariate space into mutually exclusive boxes that can be utilized to define subgroups. Conceptually the algorithm is similar to classification and regression trees but rather …

Statistical Methods For Assessing Treatment Effects For Observational Studies., Kristopher C. Gardner 1984-

Electronic Theses and Dissertations

Though randomized clinical (RCTs) trials are the gold standard for comparing treatments, they are often infeasible or exclude clinically important subjects, or generally represent an idealized medical setting rather than real practice. Observational data provide an opportunity to study practice-based evidence, but also present challenges for analysis. Traditional statistical methods which are suitable for RCTs may be inadequate for the observational studies. In this project, four of the most popular statistical methods for observational studies: ANCOVA, propensity score matching, regression with the propensity score as a covariate, and instrumental variables (IV) are investigated through application to MarketScan insurance claims data. …

Some New Probability Distributions Based On Random Extrema And Permutation Patterns, Jie Hao

Electronic Theses and Dissertations

In this paper, we study a new family of random variables, that arise as the distribution of extrema of a random number N of independent and identically distributed random variables X₁,X₂, ..., X_N, where each X_i has a common continuous distribution with support on [0,1]. The general scheme is first outlined, and SUG and CSUG models are introduced in detail where X_i is distributed as U[0,1]. Some features of the proposed distributions can be studied via its mean, variance, moments and moment-generating function. Moreover, we make some other choices for …

The Financial Crisis Was Good For Something: Improved Nonprofit Efficiency, Caitlin Paige Britt

Finance Undergraduate Honors Theses

This study explores the need for financial performance measures in the nonprofit sector and the impact the 2008-2009 Financial Crisis had upon nonprofits’ efficiency. This analysis tests the hypothesis that the financial crisis actually improved nonprofit efficiency by forcing nonprofits to eliminate unnecessary costs, continue to produce their services, thus improving operational efficiency, despite decreased donor contributions and increased user need. Entries reported on nonprofits’ IRS 990 forms from 2003-2010 determined whether nonprofit efficiency was significantly different after the crisis. The efficiencies used to measure the impact of the Financial Crisis include: Program Expense Efficiency, Administrative Expense Efficiency, Fundraising Expense …

Median Based Modified Ratio Estimators With Known Quartiles Of An Auxiliary Variable, Jambulingam Subramani, G Prabavathy

Journal of Modern Applied Statistical Methods

New median based modified ratio estimators for estimating a finite population mean using quartiles and functions of an auxiliary variable are proposed. The bias and mean squared error of the proposed estimators are obtained and the mean squared error of the proposed estimators are compared with the usual simple random sampling without replacement (SRSWOR) sample mean, ratio estimator, a few existing modified ratio estimators, the linear regression estimator and median based ratio estimator for certain natural populations. A numerical study shows that the proposed estimators perform better than existing estimators; in addition, it is shown that the proposed median based …

On The Exponentiated Weibull Distribution For Modeling Wind Speed In South Western Nigeria, Olanrewaju I. Shittu, K A. Adepoju

Journal of Modern Applied Statistical Methods

One of the bases for assessment of wind energy potential for a specified region is the probability distribution of wind speed. Thus, appropriate and adequate specification of the probability distribution of wind speed becomes increasingly important. Several distributions have been proposed for describing wind distribution. Among the most popular distributions is the Weibull whose choice is due to its flexibility. An exponentiated Weibull distribution is proposed as an alternative to model wind speed data with a view to comparing it with the existing Weibull distribution. Results indicate that the proposed distribution outperforms the existing Weibull distribution for modeling wind speed …

Robust Regression Analysis For Non-Normal Situations Under Symmetric Distributions Arising In Medical Research, S S. Ganguly

Journal of Modern Applied Statistical Methods

In medical research, while carrying out regression analysis, it is usually assumed that the independent (covariates) and dependent (response) variables follow a multivariate normal distribution. In some situations, the covariates may not have normal distribution and instead may have some symmetric distribution. In such a situation, the estimation of the regression parameters using Tiku’s Modified Maximum Likelihood (MML) method may be more appropriate. The method of estimating the parameters is discussed and the applications of the method are illustrated using real sets of data from the field of public health.

Jmasm 33: A Two Dependent Samples Maximum Test Calculator: Excel, Saverpierre Maggio, Shlomo Sawilowsky

Journal of Modern Applied Statistical Methods

An Excel Macro was created to provide researchers with an easy to use resource in order to calculate the two dependent samples maximum test as provided in Maggio and Sawilowsky (2014), which permits conducting both the two dependent samples t-test and Wilcoxon signed-ranks test on the same data while eliminating concerns related to Type I error inflation and choice of statistical tests.

Vol. 13, No. 1 (Full Issue), Jmasm Editors

Journal of Modern Applied Statistical Methods

No abstract provided.