Physical Sciences and Mathematics Commons^™

Mark-Recapture Creel Survey And Survival Models, Shampa Saha

Mathematics & Statistics Theses & Dissertations

In this dissertation, we consider a model based approach to the estimation of exploitation rate of a fish population by combining mark-recapture procedures with a creel survey. We also consider the analysis of a proportional hazards survival model for randomly censored observations, known as the Koziol-Green model. The model assumes that the lifetime survivor function is a power of the censored time survivor function.

In Chapter 2, we introduce the model based approach to the estimation of the exploitation rate of a fish population by combining mark-recapture procedures with a creel survey. We assume that in the beginning of a …

Single Row Routing: Theoretical And Experimental Performance Evaluation, And New Heuristic Development, David A. Hysom

Computer Science Theses & Dissertations

The Single Row Routing Problem (SRRP) is an abstraction arising from real-world multilayer routing concerns. While NP-Complete, development of efficient SRRP routing heuristics are of vital concern to VLSI design. Previously, researchers have introduced various heuristics for SRRP; however, a comprehensive examination of SRRP behavior has been lacking.

We are particularly concerned with the street-congestion minimization constraint, which is agreed to be the constraint of greatest interest to industry. Several theorems stating lower bounds on street congestion are known. We show that these bounds are not tight in general, and argue they may be in error by at least 50% …

Analysis Of Repeated Measures Data Under Circular Covariance, Andrew Montgomery Hartley

Mathematics & Statistics Theses & Dissertations

Circular covariance is important in modelling phenomena in epidemiological, communications and numerous physical contexts. We introduce and develop a variety of methods which make it a more versatile tool. First, we present two classes of estimators for use in the presence of missing observations. Using simulations, we show that the mean squared errors of the estimators of one of these classes are smaller than those of the Maximum Likelihood (ML) estimators under certain conditions. Next, we propose and discuss a parsimonious, autoregressive type of circular covariance structure which involves only two parameters. We specify ML and other types of estimators …

Optimality And Construction Of Designs With Generalized Group Divisible Structure, Sudesh K. Srivastav

Mathematics & Statistics Theses & Dissertations

This thesis is an investigation of the optimality and construction problems attendant to the assignment of v treatments to experimental units in b blocks of size k, paying special attention to settings for which equal replication of the treatments is not possible. The model is that of one way elimination of heterogeneity, in which the expectation of an observation on treatment i in block j is T_i + βj (treatment effect + block effect), where T_i and βj are unknown constants, 1 ≤ i ≤ v and 1 ≤ j ≤ b. All observations are assumed to …

Linear Models For Multivariate Repeated Measures Data, Shantha S. Rao

Mathematics & Statistics Theses & Dissertations

In this dissertation we focus mainly on the analysis of continuous multivariate repeated measurements data based on the assumption of multivariate normality. However certain aspects of the analysis of univariate repeated measures data are also considered. Typically, we have measurements on p variables (possibly correlated) in the form of px1 vectors y_ijk observed at k = 1,2, ...,t_ij occasions on j = 1,2, ..., n_i individuals from i = 1,2, ..., g groups. We assume a naturally occurring covariance structure V_ij ⊗ ∑ among the p variables on the j^th individual from i^th group …

Analysis Of Growth Curves Under Some Special Covariance Structures, Shobha Prabhala

Mathematics & Statistics Theses & Dissertations

In this dissertation we consider the growth curve or generalized MANOVA model in its most general form given by and develop statistical methodology for analyzing data using this model. Here g represents the number of groups, Y_ij is the observation matrix, ξ is a matrix of unknown parameters, A_i is a known matrix of rank g, and B_ij is a matrix of rank k. Further, the rows of the error matrix ∈_ij are independent and each distributed as N_pij (0, Σ_ij).This model accommodates different kinds of unbalanced data, such as, monotone data, data …

Comparing Traditional Statistical Models With Neural Network Models: The Case Of The Relation Of Human Performance Factors To The Outcomes Of Military Combat, William Oliver Hedgepeth

Engineering Management & Systems Engineering Theses & Dissertations

Statistics and neural networks are analytical methods used to learn about observed experience. Both the statistician and neural network researcher develop and analyze data sets, draw relevant conclusions, and validate the conclusions. They also share in the challenge of creating accurate predictions of future events with noisy data.

Both analytical methods are investigated. This is accomplished by examining the veridicality of both with real system data. The real system used in this project is a database of 400 years of historical military combat. The relationships among the variables represented in this database are recognized as being hypercomplex and nonlinear.

The …

Some Sampling Designs And Estimation Problems, Hassan Lakkis

Mathematics & Statistics Theses & Dissertations

In the first chapter we review some standard estimators in sampling from a finite population, and some design-based estimators in sampling from a continuous universe.

In concert with the theory initiated by professor Douglas Robson (personal communication) and later presented by Cordy (1993), we consider design-based variance estimation for probability sampling from a continuous and spatially distributed universe. Using this theory in chapter two, the sampling design of one random point from each cell of a translated grid is investigated and the problem of edge effects on estimation is illustrated with examples. Also in chapter four, standard systematic sampling methods …

Methods For The Comparison Of Timing Behavior Applied To The Pink Salmon Fisheries Of Prince William Sound, Alaska, Louis J. Rugolo

OES Theses and Dissertations

Harvest control in salmonid fisheries was examined as a problem in the formulation of regulations which restrict time and area of fishing. An ability to rigorously define and compare the form of the progression of migration across time and between harvest areas was judged fundamental to objective harvest decisions. Identification and evaluation of statistical methods appropriate to the comparison of empirical migratory time densities was performed.

The development of the measure of central tendency (mean date) of the time density as the consistent, unbiased estimator of migratory behavior was given. Practical evidence demonstrated that the mean date was highly resistant …

Invariance Properties Of Statistical Tests For Dependent Observations, Akhil K. Vaish

Mathematics & Statistics Theses & Dissertations

In this dissertation we assume that the observations are from normal populations but are correlated and study the problem of characterizing the class of covariance structures such that the distributions of the popular test statistics remain invariant, that is, they remain the same except for a constant factor. We first obtain some simple extensions and variations of the well known Cauchy-Schwarz inequality. Incidentally, several inequalities that are useful in the detection of outliers can be deduced from our results.

Our main result is a characterization of the class of all nonnegative definite solutions W to the matrix equation AWA = …

The Use Of A Factory Simulation To Evaluate A Flexible Control Structure For Integrated Manufacturing, Ling Ling Pan

Engineering Management & Systems Engineering Theses & Dissertations

Once a control structure for an integrated manufacturing system is decided upon, manufacturing activities are limited by that structure. A flexible control structure is presented as an approach for accommodating a variety of manufacturing activities, without being limited to a single control structure. A flexible control structure is one that allows multiple types of control structure in the manufacturing process. For example, both hierarchical and non-hierarchical structures may be used in a flexible structure. The properties of a flexible control structure are discussed from the point of view of graph theory.

Control structures for automated manufacturing are difficult to evaluate …

Reliability Trend Analyses With Statistical Confidence Limits Using The Luke Reliability Trend Chart, Stephen R. Luke

Engineering Management & Systems Engineering Theses & Dissertations

In electronic systems, it is interesting to understand exactly how the reliability is changing with time. Dynamic performance changes when a system passes from infant mortality stage into useful life phase and when the system passes from useful life phase into wearout phase. Dynamic performance also changes when the system is redesigned or when the system is acted on by a number of other outside forces such as a change in maintenance policy, escalation of alignment problems, or a change in training program. It is important to know when a system is changing dynamically in order to assess design, policy …

Multidimensional Approach To Implementation Of Continuous Process Improvement Utilizing Small Run Analysis In A Shipyard Environment, Paul Ray Hollandsworth

Engineering Management & Systems Engineering Theses & Dissertations

Nationally, both public and private shipyards are experiencing a high rework rate (over 40%) in the fabrication of plug connectors used for electronic systems onboard Navy vessels. The shipyard's survival depends on acquiring the elements necessary to maintain a major industry in a position of continuous improvement that produces a better product than their competitors, at less cost, in a safe manner, and on schedule.

This research addresses the complex problem of how to introduce quality control methodologies within a job shop environment that assists in identifying variables that influence the rework rate of plug fabrication process over a four …

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.

The Truncated Cauchy Distribution: Estimation Of Parameters And Application To Stock Returns, Paul G. Staneski

Mathematics & Statistics Theses & Dissertations

The problem addressed in this dissertation is the existence and estimation of the parameters of a truncated Cauchy distribution. It is known that when a number of distributions with infinite support are truncated to a finite interval that the maximum likelihood estimator of the scale parameter fails to exist with positive probability. In particular, necessary and sufficient conditions which give rise to instances of non-existence have been found for the exponential (Deemer and Votaw (1955)), gamma (Broeder (1955), Hegde and Dahiya (1989)), Weibull (Mittal and Dahiya (1989)) and normal distribution (Barndorff-Nielsen (1978), Mittal and Dahiya (1987), Hegde and Dahiya (1989)). …

Mathematical Models Of Prevascular Tumor Growth By Diffusion, Sophia A. Maggelakis

Mathematics & Statistics Theses & Dissertations

A study of several complementary mathematical models that describe the early, prevascular stages of solid tumor growth by diffusion under various simplifying assumptions is presented. The advantage of these models is that their degree of complexity is relatively low, which ensures fairly straightforward comparisons with experimental or clinical data (as it becomes available), yet they are mathematically sophisticated enough to capture the main biological phenomena of interest.

The tumor growth and cell proliferation rate are assumed to depend on the local concentrations of nutrients and inhibitory factors. The effects of geometry and spatially non-uniform inhibitor production and non-uniform nutrient consumption …

Software Reliability Models, Syed Afzal Hossain

Mathematics & Statistics Theses & Dissertations

The problem considered here is the building of Non-homogeneous Poisson Process (NHPP) model. Currently existing popular NHPP process models like Goel-Okumoto (G-O) and Yamada et al models suffer from the drawback that the probability density function of the inter-failure times is an improper density function. This is because the event no failure in (0, oo] is allowed in these models. In real life situations we cannot draw sample(s) from such a population and also none of the moments of inter-failure times exist. Therefore, these models are unsuitable for modelling real software error data. On the other hand if the density …

Detection Of Outliers And Influential Observations In Regression Models, Anwar M. Hossain

Mathematics & Statistics Theses & Dissertations

Observations arising from a linear regression model, lead one to believe that a particular observation or a set of observations are aberrant from the rest of the data. These may arise in several ways: for example, from incorrect or faulty measurements or by gross errors in either response or explanatory variables. Sometimes the model may inadequately describe the systematic structure of the data, or the data may be better analyzed in another scale. When diagnostics indicate the presence of anomalous data, then either these data are indeed unusual and hence helpful, or contaminated and, therefore, in need of modifications or …

Optimal Row-Column Designs For Correlated Errors And Nested Row-Column Designs For Uncorrelated Errors, Nizam Uddin

Mathematics & Statistics Theses & Dissertations

In this dissertation the design problems are considered in the row-column setting for second order autonormal errors when the treatment effects are estimated by generalized least squares, and in the nested row-column setting for uncorrelated errors when the treatment effects are estimated by ordinary least squares. In the former case, universal optimality conditions are derived separately for designs in the plane and on the torus using more general linear models than those considered elsewhere in the literature. Examples of universally optimum planar designs are given, and a method is developed for the construction of optimum and near optimum designs, that …

Large Deviation Local Limit Theorems For Ratio Statistics, Sanjeev V. Sabnis

Mathematics & Statistics Theses & Dissertations

Let {T„, n > 1} be an arbitrary sequence of non-lattice random variables and {S_n, n > 1} be another sequence of positive non-lattice random variables. Let the two sequences be independent. Let Ø_1n and Ø_2n be the moment genereating functions of {Tn, n > 1} and { S_n,n > 1} respectively. Let {a_n} be a sequence of real numbers such that a_n —»• oo.

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 …

Statistical Calibration Theory, James John Mckeon

Mathematics & Statistics Theses & Dissertations

A calibration method substitutes for measurements, X(,i), that are accurate but impractical or costly, a set of measurements, Y(,i), that are less accurate but simpler or less costly. There are two general types of calibration methods. The classical approach in which once the calibration sample is drawn, the estimates of the X values for a given unit is found without any consideration of the distribution of X values for the other units to be measured. This corresponds best to the literal meaning of the word "calibration". Maximum likelihood estimation is the statistical formulation of the classical approach.

The second approach …

Estimating The Parameters Of Truncated Distributions, Mukul Mohan Mittal

Mathematics & Statistics Theses & Dissertations

The problem considered here is the estimation of the parameters of some special truncated distributions. If the sample observations are restricted to the interval {O, T} with T known, then it is well known in the literature that the method of maximum likelihood fails to provide a finite estimate, for the mean of an exponential distribution, whenever the sample mean is greater than T/2 (Deemer and Votaw, 1955, Ann. Math. Statist. 26, 498-504). Not so well known is the nonexistence of the maximum likelihood estimator (m.l.e.), under certain conditions, for the scale parameter of a gamma distribution from a truncated …

An Intraseason Forecasting System For Commercial Marine Fisheries, Erik J. Barth

OES Theses and Dissertations

The reliability of an intraseason yield estimation technique which is commonly used by Pacific salmon harvest managers is evaluated for applicability to a variety of commercial finfish and crustacean fisheries. The estimation technique is known as the average timing or the average performance model. The method is not easily related to standard statistical models, but does show some similarity to both a single parameter linear regression model and the ratio estimator of sampling theory. A comparison of these models, a two parameter linear model, and a regression estimator is made to determine if the precision of forecasts of performance can …