Mathematics Commons^™

Development Of A Gamified Number Line App For Teaching Estimation And Number Sense In Grades 1 To 7, Debbie Marie Verzosa, Ma. Louise Antonette N. De Las Peñas, Maria Alva Q. Aberin, Agnes Garciano, Jumela F. Sarmiento, Mark Anthony C. Tolentino

Mathematics Faculty Publications

Fraction knowledge is known to be a gatekeeper to more advanced mathematical learning. On the basis of the literature on early number learning, a number line mobile application called Catch the Carrot was designed to develop students’ knowledge of whole number and fraction magnitude. This paper aims to describe the design of the Catch the Carrot app and discusses the rationale for using number lines as representational scaffolds for developing children’s understanding of numbers, particularly their estimation and number sense skills. The gamification features of the app, as well as strategies for integration in a classroom are also presented. This …

Finite-Time State Estimation For An Inverted Pendulum Under Input-Multiplicative Uncertainty, William Mackunis, Sergey V. Drakunov, Anu Kossery Jayaprakash, Krishna Bhavithavya Kidambi, Mahmut Reyhanoglu

Publications

A sliding mode observer is presented, which is rigorously proven to achieve finite-time state estimation of a dual-parallel underactuated (i.e., single-input multi-output) cart inverted pendulum system in the presence of parametric uncertainty. A salient feature of the proposed sliding mode observer design is that a rigorous analysis is provided, which proves finite-time estimation of the complete system state in the presence of input-multiplicative parametric uncertainty. The performance of the proposed observer design is demonstrated through numerical case studies using both sliding mode control (SMC)- and linear quadratic regulator (LQR)-based closed-loop control systems. The main contribution presented here is the rigorous …

Exploring The Variance Of The Sample Variance Through Estimation And Simulation, Christina Stradwick

Theses, Dissertations and Capstones

In this thesis, we examine properties of the variance of the sample variance, which we will denote V (S ² ). We derive a formula for this variance and show that it only depends on the sample size, variance, and kurtosis of the underlying distribution. We also derive the maximum likelihood estimators for this parameter, V^ˆ (S ² ), under the normal, exponential, Bernoulli, and Poisson distributions and end the thesis with simulations demonstrating the distributions of these estimators.

Fitting A Complex Markov Chain Model For Firm And Market Productivity, Julia Ruth Valder

Theses and Dissertations

This thesis develops a methodology of estimating parameters for a complex Markov chain model for firm productivity. The model consists of two Markov chains, one describing firm-level productivity and the other modeling the productivity of the whole market. If applicable, the model can be used to help with optimal decision making problems for labor demand. The need for such a model is motivated and the economical background of this research is shown. A brief introduction to the concept of Markov chains and their application in this context is given. The simulated data that is being used for the estimation is …

The Kumaraswamy Marshal-Olkin Family Of Distributions, Morad Alizadeh, M. H. Tahir, Gauss M. Cordeiro, M. Mansoor, Muhammad Zubair, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We introduce a new family of continuous distributions called the Kumaraswamy Marshal-Olkin generalized family of distributions. We study some mathematical properties of this family. Its density function is symmetrical, left-skewed, right-skewed and reversed-J shaped, and has constant, increasing, decreasing, upside-down bathtub, bathtub and S-shaped hazard rate. We present some special models and investigate the asymptotics and shapes of the family. We derive a power series for the quantile function and obtain explicit expressions for the moments, generating function, mean deviations, two types of entropies and order statistics. Some useful characterizations of the family are also proposed. The method of maximum …

Estimating The Extreme Low-Temperature Event Using Nonparametric Methods, Anisha D'Silva

Master's Theses (2009 -)

This thesis presents a new method of estimating the one-in-N low temperature threshold using a non-parametric statistical method called kernel density estimation applied to daily average wind-adjusted temperatures. We apply our One-in-N Algorithm to local gas distribution companies (LDCs), as they have to forecast the daily natural gas needs of their consumers. In winter, demand for natural gas is high. Extreme low temperature events are not directly related to an LDCs gas demand forecasting, but knowledge of extreme low temperatures is important to ensure that an LDC has enough capacity to meet customer demands when extreme low temperatures are experienced. …

Adaptive Stochastic Systems: Estimation, Filtering, And Noise Attenuation, Araz Ryan Hashemi

Wayne State University Dissertations

This dissertation investigates problems arising in identification and control of stochastic systems. When the parameters determining the underlying systems are unknown and/or time varying, estimation and adaptive filter- ing are invoked to to identify parameters or to track time-varying systems. We begin by considering linear systems whose coefficients evolve as a slowly- varying Markov Chain. We propose three families of constant step-size (or gain size) algorithms for estimating and tracking the coefficient parameter: Least-Mean Squares (LMS), Sign-Regressor (SR), and Sign-Error (SE) algorithms.

The analysis is carried out in a multi-scale framework considering the relative size of the gain (rate of …

Statistical Methods For Nonlinear Dynamic Models With Measurement Error Using The Ricker Model, David Joseph Resendes

Open Access Dissertations

In ecological population management, years of animal counts are fit to nonlinear, dynamic models (e.g. the Ricker model) because the values of the parameters are of interest. The yearly counts are subject to measurement error, which inevitably leads to biased estimates and adversely affects inference if ignored. In the literature, often convenient distribution assumptions are imposed, readily available estimated measurement error variances are not utilized, or the measurement error is ignored entirely. In this thesis, ways to estimate the parameters of the Ricker model and perform inference while accounting for measurement error are investigated where distribution assumptions are minimized and …

The Effect Of Endpoint Knowledge On Dot Enumeration, Alex Michael Moore

UNLV Theses, Dissertations, Professional Papers, and Capstones

This study attempts to extend the principle tenets of the Overlapping Waves Theory (Siegler, 1996), a framework designed to explain the progression of trends in cognitive development, to adult participants’ performance in a dot enumeration task. Literature in the 0-100 number line estimation task (Siegler & Booth, 2004, Ashcraft & Moore, 2011) has revealed a pervasive trend in child estimation such that young children (especially those in kindergarten) respond with a logarithmic line of best fit, while children at the third grade and above overwhelmingly respond with linear estimates to this same range of numbers. A similar developmental trend is …

Statistical Properties Of A Convoluted Beta-Weibull Distribution, Jianan Sun

Theses, Dissertations and Capstones

A new class of distributions recently developed involves the logit of the beta distribution. Among this class of distributions are the beta-normal (Eugene et.al. (2002)); beta-Gumbel (Nadarajah and Kotz (2004)); beta-exponential (Nadarajah and Kotz (2006)); beta-Weibull (Famoye et al. (2005)); beta-Rayleigh (Akinsete and Lowe (2008)); beta-Laplace (Kozubowski and Nadarajah (2008)); and beta-Pareto (Akinsete et al. (2008)), among a few others. Many useful statistical properties arising from these distributions and their applications to real life data have been discussed in the literature. One approach by which a new statistical distribution is generated is by the transformation of random variables having known …

On Sequential And Fixed Designs For Estimation With Comparisons And Applications, Mekki Terbeche, Broderick O. Oluyede, Ahmed Barbour

Department of Mathematical Sciences Faculty Publications

A fully sequential approach to the estimation of the difference of two population means for distributions belonging to the exponential family of distributions is adopted and compared with the best fixed design. Results on the lower bound for the Bayes risk due to estimation and expected cost are presented and shown to be of first order efficiency. Applications involving the Poisson and exponential distributions with gamma priors as well as the Bernoulli distribution with beta priors are given. Finally, some numerical results are presented.

Simulation Study Of Estimation And Inference In Factor Analysis: Normal And Non-Normal Noise Distributions, Ping Zhang

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Objective: To study the estimation and inference m factor analyses when the data have normal or non-normal noise distributions.

Methods: Population data were created in package R with a specified number of factors, factor structure and observable variables with known loadings. Then, repeated simple random samples (SRS's) were taken from the population, independently. The maximum likelihood method with varimax rotation was used to perform factor analysis and inference on each sampled dataset. Factor loadings were estimated to determine if the estimation of the loadings was (approximately) unbiased and/or efficient for each specified population and chi-square x2-statistics were obtained to test …

Estimation, Testing, And Monitoring Of Generalized Autoregressive Conditionally Heteroskedastic Time Series, Aonan Zhang

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

We study in this dissertation Generalized Autoregressive Conditionally Heteroskedastic (GARCH) time series. The research focuses on squared GARCH sequences. Our main results are as follows:

1. We compare three methods of constructing confidence intervals for sample autocorrelations of squared returns modeled by models from the GARCH family. We compare the residual bootstrap, block bootstrap and subsampling methods. The residual bootstrap based on the standard GARCH(l,1) model is seen to perform best. Confidence intervals for cross-correlations of a bivariate GARCH model are also studied.

2. We study a test to discriminate between long memory and volatility changes in financial returns data. …

Generalized Minimum Penalized Hellinger Distance Estimation And Generalized Penalized Hellinger Deviance Testing For Generalized Linear Models: The Discrete Case, Huey Yan

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In this dissertation, robust and efficient alternatives to quasi-likelihood estimation and likelihood ratio tests are developed for discrete generalized linear models. The estimation method considered is a penalized minimum Hellinger distance procedure that generalizes a procedure developed by Harris and Basu for estimating parameters of a single discrete probability distribution from a random sample. A bootstrap algorithm is proposed to select the weight of the penalty term. Simulations are carried out to compare the new estimators with quasi-likelihood estimation. The robustness of the estimation procedure is demonstrated by simulation work and by Hapel's α-influence curve. Penalized minimum Hellinger deviance tests …

Parameter Estimation By Conditional Coding, Taylor Duersch

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Conditional coding is an application of Markov Chain Monte Carlo methods for sampling from conditional distributions. It is applied here to the problem of estimating the parameters of a computer-simulated pattern of fractures in an isomorphic, homotropic material under plane strain. We investigate the theory and procedures of conditional coding and show the viability of the technique by its application.

Estimation In A Marked Poisson Error Recapture Model Of Software Reliability, Rajan Gupta

Mathematics & Statistics Theses & Dissertations

Nayak's (1988) model for the detection, removal, and recapture of the errors in a computer program is extended to a larger family of models in which the probabilities that the successive programs produce errors are described by the tail probabilities of discrete distribution on the positive integers. Confidence limits are derived for the probability that the final program produces errors. A comparison of the asymptotic variances of parameter estimates given by the error recapture and by the repetitive-run procedure of Nagel, Scholz, and Skrivan (1982) is made to determine which of these procedures efficiently uses the test time.

Estimation In Truncated Exponential Family Of Distributions, Laxman M. Hegde

Mathematics & Statistics Theses & Dissertations

Estimating the parameters of a truncated distribution is a well known problem in statistical inference. The non-existence of the maximum likelihood estimator (m.l.e.) with positive probability in certain truncated distributions is not well known. To mention a few results in the literature:

(i) Deemer and Votaw 1955 show that the maximum likelihood estimator does not exist in a truncated negative exponential distribution on 0,T , T > 0 known, whenever the sample mean x (GREATERTHEQ) T/2.

(ii) Broeder 1955 shows that the maximum likelihood estimator of the scale parameter of a truncated gamma distribution, with the shape parameter being known, becomes …

On Finite Element Methods For The Euler-Poisson-Darboux Equation, Anatoly M. Genis

Mathematics and System Engineering Faculty Publications

We deal primarily with the derivation of various convergence estimates for some semidiscrete and fully discrete procedures which might be used in the approximation of exact solutions of initial-boundary value problems with homogeneous Dirichlet boundary conditions for the Euler-Poisson-Darboux equation. Although the equation is of hyperbolic type, the results are somewhat analogous to those known for parabolic equations, due to the presence of a limited 'smoothing' property. This paper contain L//2 estimates, maximum norm estimates, negative norm estimates, interior estimates of difference quotients and superconvergence estimates of the error.

Sequential Methods In Estimation And Prediction., Nitis Mukhopadhyay Dr.

Doctoral Theses

No abstract provided.

A New Confidence Interval For The Mean Of A Normal Distribution, David Lee Wallace

All Master's Theses

A typical problem in statistical inference is the following: An experimenter is confronted with a density function f(x; ϴ) which describes the underlying population of measurements. The form of f may or may not be known, and ϴ is a parameter (possibly vector-valued) which describes the population. The statistician's job is to estimate or to test hypotheses about the unknown parameter ϴ. In this paper, we shall consider interval estimation of the mean of the normal density function.